That is accurate. You do not even have to speak to Animal Crossing Bells the person who has the bubble. When it's that the"go out" bubble, it is going to select a random villager every day. It can be the exact same villager or a villager that is"within" (so that you don't see the bubble), but it will still be a randomly chosen villager, and all them are eligible (technically there's a few exceptions associated with home moving and birthdays).
The move-out bubble itself is on a cooldown that's two weeks since you've had a move-out dialog, so in the event that you have the dialogue (no matter what you tell the villager to do) it resets. But if you ignore it, then it is going to jump around every day.
Would you have to force you to move outside or simply reject an older one's move out request? I'm like 99% sure that I got my latest villager to Nook Miles Ticket For Sale move out once, but I think maybe 2-3 villagers requested to move out (but I told them to not ) before she did. I came back in January after not playing because around this time this past year and was extremely disappointed purchase the lack of items added, and notably the absence of"new to the series" things added. The ocean update was cool, the art update was nice but the lack of QoL updates is what killed the game for me personally. Fishing Bait still only being able to be produced one at a time.