Does anyone have helpful tips on introducing a new kitten to older cats? We are on day three with a new kitten (12 weeks old). He is not shy or timid about the room he is currently being kept in. He doesn't hide when either my fiancé or I walk in; he snuggles up to us and rubs against us when we are in the room with him. If it were just him, I would feel fine letting him be free at this point, with how he is acting.
However, we have two older cats, and we had a baby gate up in the room he is being kept in so they could see him. They will watch him and be curious until he comes to the gate, and then they hiss/growl. I understand early on that it's pretty normal. He has escaped once because he figured out he could climb over the gate (the second gate to block the whole doorway is on its way), and while none of the other cats were aggressive, it was clear that one of them was very uneasy/stressed when he was running around. Of course, he's a kitten, so he did not care one way or the other, and when he got too close to her, and she hissed, he backed away.
Any tips beyond the usual ones for making an easy transition for all the cats involved? I swapped out the blanket he was sleeping on for one of our other cats so they could both get used to the scent. Everyone has their own food and litter boxes. Is it just give it time and keep them separated till they are used to the other cat existing in their house?