Tobirama is claimed by a dragon daiyoukai. He is later menaced by a omukade. Dragons and omukade are enemies, according to real life legends.
Hashirama's belief Tobirama is going through a rebellious stage at first simply looks like him not knowing what's actually going on but he is actually justified. Look at Tobirama's recent activities. He's taking up wearing prayer beads and he prays regularly (to feed Churippu) and he is learning how to play the koto. Most people wouldn't view these as rebellious. But Butsuma is the sort of person to hate the notion of praying instead of just taking care of things yourself and he dislikes wasting time so an hobby that has no practical purpose would irritate. And Hashirama knows Tobirama well enough to realize if he ever rebelled, it would be in a way that doesn't look like rebellion. So it's actually a logical conclusion, given what his father and younger brother are like.
