So it can be played in Bant, Bant, Bant, and Bant?
It can be played in either Azorius or Selesnya and be literally the only card that is an outlier - 1 card out of 60 in Duels (2-4 cards in a constructed environment), and probably supported entirely by dual lands that will have little to no effect on the viability of playing the WG or WU cards in the deck (I doubt I'd even add 1 island, or forest). It will probably not even effect the consistency of the mana base at all. That is definitely not what I'd call a Bant deck unless I was just trying to be technical just for argument's sake. You'll probably see it in Standard after the next set, btw, when the Selesnya Tokens deck starts splashing U just for Tamiyo - I'd bet they still call it Selesnya Tokens if they do, btw, same as I am doing right now.
Splashing in a third color will of course affect the consistency of the mana base.
And I don't care what they want to call it, it won't be Selesnya Tokens, just like Jeskai Black isn't Jeskai. Unrelated to colors, but when Dralnu Du Louvre cut Dralnu it kept the name, because that was the name of the initial shell. The name isn't what is important. A deck running W, U, and G cards is a Bant deck. That's just it's color designation.
(EDIT: And not for nothing, because it's related to a separate argument, but Cryptic Command shows up in plenty of two color and even a few three color decks. Duels wouldn't be able to consistently pull that off, but Standard and Modern certainly can with the right sets.)
Splashing a third color will have a negligible effect on the consistency of the mana base if it has no effect on the number of sources of the two primary colors, which will be the case in both Selesnya Humans, and Azorius Fliers - both of which are decks which are likely to splash for Tamiyo. If you consider both of those decks Bant after the splash, I hope you realize that we are having a semantics discussion. Shall we also argue about the proper way to spell the word color/colour, because this is a waste of both of our times. You'll be able to run Tamiyo in either of those extremely different decks, and you'd be able to do so in standard with similarly minimal effect (even at 4 copies). A 1UUU card (at 4 copies) needs about 20-25 sources of U Mana, that's almost the entire deck - You can't splash for it, but (as you mentioned) you might be able to splash out of it.