Paladin auras "originate" from their entire space, so the radius extends from the edge of their space
In this case, Mike Mearls' interpretation in your second link is incorrect, in addition to not being an official ruling (which is good, considering Mearls' tweets rarely have any basis in the rules).
All of the paladin auras don't specify a "point" of origin; instead, they merely specify that certain effects apply to creatures "within 10 feet of you". (At 18th level, the range of your auras increases to 30 feet.) In essence, it's an "area of origin" rather than a single point.
For instance, the description of the paladin's Aura of Protection feature states:
Starting at 6th level, whenever you or a friendly creature within 10 feet of you must make a saving throw, the creature gains a bonus to the saving throw equal to your Charisma modifier (with a minimum bonus of +1). You must be conscious to grant this bonus.
And the description of the Aura of Courage feature says:
Starting at 10th level, you and friendly creatures within 10 feet of you can’t be frightened while you are conscious.
(Most of the subclass options also grant their own auras at 7th level.)
Logically speaking, it would make no sense to say that a creature right next to a Large or Huge creature is not "within 10 feet of it". Thus, an aura is an effect that does not have a point of origin; it originates from you and your space as a whole.
Rules designer Jeremy Crawford addressed a question about the area/range of a 10-foot paladin aura in this pair of unofficial tweets from March 2016:
Which is correct representing the area of paladin aura (10 ft)?
Is each square 5 ft., and which aura are you talking about?
Yes, each square is 5 ft. I meant Aura of Protection and Aura of Courage. Thanks.
Aura of Protection/Courage extends 10 ft. all around. (None are correct, unless your circles are polygons.)
In that example image:
- option A treats the aura as if it originates from the center of the
creature's space
- option B treats it as if it were a spell, originating from a corner
of the grid adjacent to the creature
- option C treats it as if it extends from the edge of the creature's
space, but inaccurately depicts the circular aura
Crawford's response suggests that C is the closest to being correct, but is wrong because of the way it depicts the area of the aura as a polygon instead of a circle.
(Also, even if the DM did decide to have the aura be square instead of circular since they're playing on a grid, the diagonals in C are too short.)
This interpretation is further supported by Crawford's reasoning in this series of unofficial tweets from May 2018 as to why the centaur and minotaur playable races (originally released for playtesting in Unearthed Arcana: Centaurs and Minotaurs at the time) should mechanically remain Medium like all other playable races instead of Large:
Visualizing one of @JeremyECrawford's reasons why Centaur and Minotaur should not be Large PCs: a 5' aura is 50% bigger and a 10' aura is 33% bigger.
That's exactly right.
Is it safe to assume we shouldn’t expect Large PC races?
Yep.
In short: Paladin auras extend from the edge of the paladin's space, not from any individual point.
For a Medium creature, a 10-foot aura is a circle over a 5×5 area on a grid (with 5-foot squares); for a Large creature, that same aura is a circle over a 6×6 area on the grid.
Best Answer
As someone who is in the middle of writing a third-party class based on around such effects, let me tell you,
It’s a mess, no one knows for sure, and Paizo refuses to clarify.
Generally, areas are measured from grid intersections; that is the rule. You choose the corner of a given square to be the spell’s origin. By this approach, emergency force sphere produces a typical 5-ft. radius effects, that is, a 10-ft. square on the standard grid.
This is nonsense, because it doesn’t really jibe with “centered on you” if it’s really off to the side. It’s not at all clear that “centered on you” shouldn’t be some sort of exception to the rule, perhaps as ShadowKras’s answer suggests, using the center of a square as the origin instead of using a grid intersection. That means you have a very, very weird overlay of a circle on the grid, where no grid lines are actually tangent to the circle at all, but rather halfway between one square and the next. Since only the originating square is covered, and the others around it are less than half covered, this causes the very weird case of a 5-ft. radius only covering one 5×5 grid square, where in every other case it covers a 10×10 square.
To make matters worse, if the caster is Large or larger, the spell won’t entirely cover the caster at all. Luckily, sort of, Paizo issued an FAQ about centered effects:
So for a Large creature, emergency force sphere covers the 10×10 space of the creature, plus 5 feet in every direction from that space: making the area look like a cross of two 15×25 rectangles (equivalently, a 25-ft. square missing 5 ft.2 in each corner).
But that FAQ only specifies “such a creature,” referring back to the question’s “Large or larger creature.” That means Medium creatures aren’t explicitly covered. Which leaves back with the unclear situation we had to begin with, but now with another possibility: maybe the FAQ should apply to them.
Because, you know, that would be consistent, and it’s certainly what a lot of groups do intuitively. The rules weren’t any different in 3.5e (and that didn’t even have an FAQ suggesting any such thing for any creatures), and yet that’s what people did in that edition too. Both options for forcing the 10-ft.-diameter circle to fit on the grid fail to capture the intuitive sense of energy emanating from the caster. Having it be space + radius out from that space makes a lot of intuitive sense; then the radius just means that creatures within that distance from you are covered.
And plus, that’s just what an FAQ is, or at least is supposed to be. It’s supposed to be explaining the rules as they are, not changing them or adding to them. If this was what they always meant for Large or larger creatures, it must also be what they meant for Medium or smaller creatures—the original rules don’t specify that the two should use separate rules. Paizo has a really, really poor track record when it comes to using the FAQ properly, but in this case I think they really probably did mean for this to be the general rule.
Mark Seifter doesn’t like that, though, and he was specifically discussing emergency force sphere:
He sounds very certain about that, and he should know. On the other hand, that’s counter-intuitive, and inconsistent with what happens with Large and larger creatures—having the rules suddenly completely change at larger sizes is just bizarre. Frankly, I have a very hard time taking him seriously on that, considering everything else. I think he is wrong. And I also should know.
The only part of that post that does make sense, to me, is the statement that emergency force sphere is too powerful. That’s absolutely true. Emergency force sphere is preposterously overpowered, and Paizo is bad and should feel bad for having ever printed it. Doubt it? Consider 3.5e’s wings of cover, which blocked a single attack as an immediate action—itself a spell frequently banned, and if you need to see why, consider this red dragon leveraging it pretty well. Now remember that emergency force sphere is dramatically more powerful.
Anyway, the long and short of it is that this is still a contentious, confusing part of the rules that desperately needs clarification, but Paizo apparently considers the matter closed and refuses to address these issues any more.
Suggestion: apply FAQ to all sizes, ban emergency force sphere
That is, the radius of centered effects always refers to the “distance from the caster’s space,” and so uses consistent rules regardless of the caster’s size. Then, because emergency force sphere was already overpowered and this makes it just more overpowered, ban it because it’s toxic and bad for the game.
This is what I’ve done in my games, and it’s also the solution I’ve taken for my work: instead of using “centered on you,” which should be exactly what I want and easily understood, I have been forced to rewrite every area to spell out that this is what I mean, and to avoid the whole “centering” thing altogether. It’s a shame, and I have no doubt that many readers will see it, and be confused why I didn’t just say “centered on you,” but this is the situation we have to live with.