Oh look, a field I'm experienced in!
The answer is no. They cannot 'possess' anyone without consent. Also, if you're looking for something to program, try a servitor, not a tulpa. You can program them to do anything you like, because they are not sentient and have no free will of their own, unlike tulpas, which are sentient and have their own free will.
Many tulpamancers (people who have tulpas) view it as a psychological phenomenon anyway, where you create another entity within your mind/body. In this case, switching or possessing could occur in the host if both parties collaborate. Let me emphasize that: If both parties collaborate. A tulpa cannot suddenly assume control of their host.
I personally view it as both psychological and metaphysical. In a metaphysical sense, by spending time with your tulpa and giving them attention, you contribute to their overall energy/presence. They exist only in the astral plane, and though they can grow strong, they cannot leave their host and are always somewhat reliant on them for energy. I wouldn't call it parasitic, but only because I'm too attached to my three 'parasites.'