Nakamura castles with two hands. But I saw one of my students taking their king and "tipping" their rook towards f1.
Is this USCF/FIDE legal?
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Nakamura castles with two hands.
That's actually illegal:
4.1 Each move must be played with one hand only.
As for your student, there's no rule that you are not allowed to simultaneously move two pieces at once, and since the rules do not describe exactly how the king and rook reach their final squares, this is up to the player. In any case, this is not a violation of rule 4.4.2:
4.4.2 [If a player having the move:] deliberately touches a rook and then his king he is not allowed to castle on that side on that move and the situation shall be governed by Article 4.3.1
4.3.1 one or more of his own pieces, he must move the first piece touched that can be moved