Infected Sims in other worlds I actually would expect because they would've been infected anyway. Traveling wouldn't cure them.
I agree that vines shouldn't be appearing in other worlds, but now realizing that you play rotationally, I can see how it could happen. :/ I don't know if they were taking into account rotational play when they said it wouldn't spread to other worlds. I think they might have been leaning more towards you wouldn't just go into a save in another world and it start happening.
Did your Sim become possessed before you rotated to another household? I would hope even with rotational play, your Sims wouldn't become possessed even while not under your control. That is really messed up. :s