Captain Zoom
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I can't find any explicit answer. My inclination is to say yes. My reasoning is that Hunter's Tactics simply says:
"At 3rd level, the hunter automatically grants her teamwork feats to her animal companion. The companion doesn't need to meet the prerequisites of these teamwork feats."
It doesn't say your "bonus teamwork feats" or "teamwork feats granted by this class". As such, if the Hunter used his normal feats (at every odd level) to take additional teamwork feats, I'd let those apply to the animal companion. Given that, if you multiclass like you propose, I'd have to agree that any teamwork feats you gain from that source also apply to the animal companion. In other words, I read the Hunter's Tactics ability as being agnostic.