Do Aniimo have branching evolutions?

Two options means the split is something you cause, not something you reach. A branching Aniimo does not pick its form from its level. It picks from the conditions you met on the way: what you decided during its quest, and what you were holding when the evolution came due. Two players can raise the same species and finish with different creatures.

The item half of that is worth planning around, because the supply is combat. Defeating a Gamma or Nova stage Aniimo gives a chance at evolution stones, so building a stock means fighting the later stages instead of catching them. Some drops are species-specific. Beating a Gamma-stage Flameruff rather than capturing it has a low chance to drop an Unbroken Flameruff Spirit in place of an ordinary evolution stone, which is a real decision at the moment you meet one. Conditions are not always items and dialogue, either. Certain Aniimo only trigger a specific evolution after being traded to another player, so that path needs a second person.

A branch can take days, not minutes

Inferlupa is reached by evolution, and the questline behind it spans three real-world days. Its mission stages sit behind daily server resets, so there is no way to compress it into one session no matter how much you have prepared. If you are working toward a branch like that, treat the decision as something you commit to early rather than something you settle on the evening you want the result.

Emberpup evolution

The fire line is the one most people ask about, and it is the clearest look at how branching plays out. Emberpup is identified as evolving into Infernal Lupa. It is also identified as evolving into Flameruff, on a line that continues to Scorchhowl, written in some places as Scorch Howl. Flameruff's Gamma stage is the one that can drop the Unbroken Flameruff Spirit, which ties the item economy above directly to this line.

Not settled: Emberpup's own line is not settled. Whether Infernal Lupa and the Flameruff route are the two halves of one branch, or a difference between builds, is still open.