I don’t recall Tink being banished to Neverland, only losing her wings. Not sure if it was ever actually explained how she ended up there.
Right, we never actually saw how Tink ended up in Neverland. Blue just took away her wings and abandoned her. I don’t think it was ever explained when and how Tink went to Neverland. In fact, Cora mentioned running into her in “Mother”, which was how she found out about Regina’s true love being Robin Hood.