Did you call it right? Sure! It's your job to bend the rules or those you don't agree with to make it fun and enjoyable and reward clever tactics.
Did you do precisely what the written rules dictate? No.
Here is why:
Divine Sense
Until the end of your next turn, you know the location of any.....not behind total cover. You know the type of being whose presence you sense, but not its identity.
'Location' or: A creature's 'Space' PHB pg. 191
A creature's space is the area in feet that it effectively controls in combat, not an expression of its physical dimensions. A typical creature is not 5ft wide, but controls a space that wide.
Mirror Image
Three Illusory duplicates appear in your space. The duplicates move with you and mimic your actions, shifting positions so it's impossible to track which image is real... A creature is unaffected if it can't see, if it relies on... blindsight or if it can perceive illusions as false, as with truesight.
Now that I've cut these down to the parts we should be paying attention to, we are left with the following conclusion with no real argument to the contrary:
A humanoid celestial angel is perhaps 2 foot across in width, but it controls a space of about 5 feet. That's its personal space, its combat space. A humanoid is not 5ft wide folks. This is its location. That particular 5ft space within its control.
Mirror Image places 3 illusory images of that same celestial in that same space. The same location. They move with the celestial, nearly imposing themselves with the celestial as to make themselves seem like an after image. Think of this as someone moving their hand in front of a high speed lens and leaving behind an after image of their hand that follows split seconds behind their real hand. A mirror image as the namesake of the spell suggests, making it impossible to track which image is real. What the spell is saying it DOESN'T do is create 3 copies of the celestial that all stand around/beside/next to said celestial like "Hi, how are you doing, which one of us do you want to hit?"
Divine Sense allows the Paladin to open up his senses and divine the location, the effective space, of a celestial that is not behind total cover. They know for all intents and purposes that there is a Celestial in that effective space, that location, but they can't identify the celestial specifically. Just that it exists.
Let's put this into the setting.
There is a Celestial that seems to be moving so fast that there are 3 other images of itself that mimic its every move and action. I can't tell which one is the right one because they are so close together in its space, its location.
The Paladin uses Divine Sense. "Yep, there's definitely a Celestial right there, but because the mirror images are mimicking its every move so closely together in its space (its 5ft location), I can't really help pinpoint which one is real. Swing and hope you hit something!"
Lesson: Divine Sense is helpful for finding invisible creatures of the effected creature type, or figuring out if there is one in disguise parading around in some other form. Something that counters magic, such as Dispel Magic, is better for something like Mirror Image, as are AoE attacks.
Not likely, but a case could be made for it
This is a bit of a tricky area, but in general we have go with the idea that things do what they say they do and no more. As with all things 5e, a DM can choose to view it differently, but looking at it through a RAW lens implies that the Paladin would still suffer the effects.
The case for Infestation
As I stated above, in 5e things (like spells) generally do what they say they do and no more. There is no clause in the Spawn of Kyuss that states that creatures immune to Disease are immune to the effects of the Spawn.
In addition, the Spawn of Kyuss doesn't state that it is a Disease. Just that using something that cures Disease will force them to wither away.
The case for Immunity
This piece comes from the viewpoint that much in the same way that a creature who is immune to certain conditions (like Charmed) makes them immune to spells that cause that such a condition.
There are a myriad of examples that show that being immune to a condition makes you immune to an effect (e.g., creatures immune to Frightened are not affected by a Vengeance Paladin's Abjure Enemy). Or that creatures immune to Charm are not affected by spells/abilities that Charm them.
The logic here is that if curing a disease kills the Spawn, and a paladin is immune to disease, then why would this 'disease' be active in it's body?
It's a reasonable step, but it isn't totally supported by RAW. A DM could houserule that as there is some sense to it, but I do not believe this to be RAW, however it may be intended.
Best Answer
As you say: the game makes no such distinction between mundane and magical diseases with this ability, with all diseases just being diseases as far as it's concerned. Divine Health will protect you from both the measles and death dog saliva, equally.
This is congruent with how Paladins' miraculous healthiness works in many prior editions of the game too, so it's certainly not an oversight to not distinguish between mundane and magical disease.
Aside, the game otherwise does make a distinction between magical and mundane diseases (see the descriptions of spells like raise dead and resurrection) but Divine Health doesn't discriminate and defeats them all.