I did what you are trying to do quite recently with one of my villagers who had a bad plot. Yes, they do plot immediately the next day.
I had 10 villagers and I wanted to move Ken around. I kicked out Ken with Phoebe's card. The very next day, Ken's house disappeared and Phobe's plot appeared. Plot Phoebe into place using the plot resetting method (starting up a new character, etc etc.). Deleted my alt character, moved on with mayor. The day Phoebe's house showed up (the day you greet her). Once you see her plot, you can summon another character.
Anyways, every time you summon a card in, invite a villager naturally, or invite from the campsite, you should always just start a new alt just to be sure. Even if their plot doesn't appear the next day, at least you will be safe :> Just keep making a new character until the plot appears.
edit
also you can be strategic with your plot resetting. amiibo villagers are known to get "stuck" (they rarely ask to move and sometimes even move into old villager spots constantly and not the desired spots unless they are covered). so if you can, wait till others move out naturally. that way you can ensure you cover up their old spots. or at least make sure you load your game before the day starts so you can cover their spot.