First up, the RAW. This is pretty simple: Divine Sense works on celestials, fiends, and undead. Player characters are all humanoids (see page 11 of the PHB), and the Tiefling traits do not say anything about making the character a fiend in any way.
Next, we have the lore. In 3.5e, tieflings were the descendants of actual fiends, whereas in 5e, they are simply a race that has had the essence of Asmodeus infused into their bloodline. So they're a bit less fiendish than they used to be. If we look at the fiend type in the Monster Manual, it says that
Fiends are creatures of wickedness native to the Lower Planes.
Tieflings definitely don't fall under this category lore-wise, because they are a humanoid race native to the Material Plane.
Trying to argue that abilities that work on fiends should work on tieflings is like trying to argue that abilities that work on dragons should work on dragonborn, but what you have to remember is that fiends are the physical embodiment of evil. The differences between tieflings and real fiends are insurmountably greater than the differences between dragonborn and dragons.
The taint in the tiefling bloodline is a devilish one, so if they were fiends, they would be devils. Taking a look at the description of devils in the Monster Manual, we see that
Devils personify tyranny,
and that
Devils live to conquer, enslave, and oppress.
The fact that tieflings are allowed to be any alignment contradicts this, and similarly, tiefling characters are allowed to do things other than conquer, enslave and oppress - they're definitely not devils.
Finally, if another argument is needed, Jeremy Crawford agrees that tieflings are humanoids, not fiends, and can't be sensed by a Paladin's Divine Sense.
XGtE is optional
It's important to remember that most of XGtE's content comprises optional rules, and this particular section on character generation is no exception. In fact, the opening on page 61 explicitly states:
IDEAS, NOT RULES
Even though these pages are full of tables and die rolls, they don’t make up a rules system — in fact, the opposite is true. You can use as much or as little of this material as you desire, and you can make decisions in any order you want.
Stretching that a little, we could infer it to mean that despite what might be implied by the options presented here, none of it should be taken as informing the actual rules of the game. It definitely doesn't help that this section of Xanathar's does contradict the racial history given for tieflings in their own description in the PHB. But if we want to take the content as presented and try and make it work, we could consider the variability of genetic expression.
All cambions are half-fiends (but not all half-fiends are cambions)
Simply put, though a cambion is a half-fiend and is always the result of union between a fiend and a humanoid, the union of a fiend and a humanoid does not always result in a cambion. Sometimes, when a devil and a humanoid procreate, perhaps the result looks more like a tiefling.
To draw a crude analogy to the real world, children of mixed race parents can vary wildly between strongly expressing the racial characteristics of one or the other parent or appearing somewhere in between - depending on exactly what random bits of genetics get passed on and in which combination. It's not even unusual for children from the same parents to appear to be completely different races!
Obviously the genetics of a fantasy world are much more complicated than ours could conceivably be (especially when you allow for magical factors). It is not much of a stretch to imagine that the children of a devil/humanoid pairing may sometimes express much more of their fiendish heritage (producing a cambion) and sometimes less (producing a tiefling).
What's the difference?
The general difference between a tiefling and a cambion is that a cambion is a very strong expression of fiendish ancestry that perhaps you can only get with one directly fiendish parent, but a tiefling is a much lesser expression of such ancestry which can also occur in descendants far removed from the original fiendish influence.
Best Answer
In D&D lore, there are indeed tieflings of races other than human. The stats in the Player's Handbook represent human-tieflings, but this does not preclude the possibility that there are others. Ultimately, the tiefling's human-centered nature is a leftover from AD&D 2nd edition, which was considerably more human-centric than later versions of D&D.
In the Forgotten Realms setting, elf-tieflings are known as fey-ri. They are the result of a house of gold elves breeding with demons to create powerful heirs. The tanarukk are orc-tieflings, a race bred for war. Both appeared in Monsters of Faerûn (2001). The wispling is a halfling-tiefling of demonic descent. The maeluth are infernal dwarf-tieflings. Both of these appeared in Fiend Folio (2003).
To stat these up in D&D 5th edition rules (I am unaware of any official 5th edition product which has done so yet), there are three easy approaches:
In order to customize these further, the Unearthed Arcana articles That Old Black Magic and Fiendish Options include variant types of tieflings.