Do I need to be influential with my human teammate to win Tourism Victory?

First, I have no idea. But after firing up a test game with me and an AI in a team (with 4 other AI players) the evidence seems to indicate you do need to influence your teammate.

First, the victory screen shows my teammate as one of the 'targets' in the cultural victory progress:

Second, the culture overview screen for victory indicates I'm influential with 0 of 5 other civilisations, implying I need to influence my teammate as there's only 4 other players.

I'm not claiming this is a definitive answer, but until we've some strong evidence (someone winning or not when all players except their teammate are influenced) this is probably the best we've got.