Do we still have as long as we like to fill the starter houses on mystery islands?

[Lotusblossom]

I'm curious because I'm relying on this for when I reset

 

[InstantNoodles]

I assume so as long as you TT to stay on the same day...?

 

[Piggleton]

I believe so, as long as you don’t complete the plots and their required furniture. Haven’t heard otherwise yet!

 

[WaileaNoRei]

Unlike with plots after the campsite is built, for the first three villagers you can still search indefinitely without time travel as long as you have not laid out any plots yet. Once you set out the plot you have one day, as usual. But there will be villagers on all mystery islands in the beginning, without you having plots set out. The villagers you find will all be lazy, normal, and peppy type (I’m sure you know this already, but just in case). As you invite each type you will stop seeing other villagers of this type, so it is a good opportunity to find a specific villager of one of these types (But they will end up in a starter house).
I know someone who started the game within the last three weeks and it worked the same as when I started.