I have been wondering this too, but after having taken in villagers to my town and then transferred them to my second town I don't think it ever stops I just think it may change to talking about most recent last town they were in..but unfortunately I haven't seen one fully integrate and never talk or sing old town stuff.
Get rid of them, void them, and cycle for them to come back. Lol, I think that's the only way.
Rhonda and Beau, who were villagers from another town that went to my town still mention about their old towns (Rhonda went to 2, Beau went to 3?).
I don't think they do. I've had a couple from another town, Marina never mentions it so I don't know if she just wasn't there long enough or wasn't treated well. The other is always mentioning their previous town, singing the tune, etc. I know she was there for a long time and she was very well loved so maybe that is the difference?
I'm hoping with time it will become less and less.
Villagers in the campsite are generated by the game - so are 'original' and have not been in another players town.
I have 3 villagers that have come via streetpass and all have mentioned their previous town and sung their old town tune, but its rare, most dialog with them is normal, so I don't find it an issue. Maybe I don't talk to them enough, but they hardly mention their previous towns. Admittedly I didn't like it when one said to me he really liked his last town.
If the villagers are good and you like them apart from that, well I wouldn't make a specific effort to get rid of them.
My villagers still talk about their previous towns and it's kinda annoying that they talk and sing about it all the time. I kinda wish they did stop talking about their other towns. Honestly, it's one of the things I dislike about the game.
They'll never stop. It's like when someone visits your town and talks to your villagers. Even if it only happened once two years ago, they'll randomly mention meeting so-and-so "the other day." That's why I don't invite people over since I reset my first town. The only vistors who talk to my villagers are my characters from my other town. I don't mind them talking about "me." LOL
My villagers have never completely stopped talking about their town, but it has gotten rare. Pietro used to talk about his old town all the time but now it's rare.
It seems to happen less frequently the longer they live in your town. I remember Flurry used to ALWAYS talk about her old town, but now it's pretty rare for her to mention it anymore.
I've also come to realize that even if I had/have a villager that I adopted and had them bounce between my towns, they'll still occasionally talk about their old-old town and/or mayor.