Yes. My kitten watches me clean it then jumps in as soon as I finish.

They wait for a clean box, would you not do the same thing?

Sometimes.

I use a system of a grate over the litter. On top of the grate goes paper towel. If I'm lucky the towel catches the poo to enable dropping down the toilet. Otherwise, it is a wash time and as the poo is frequently soft these days a clean of the litter.
I hope the paper towel prolongs the life of the litter which can get quite rank in hot weather.
And yes, fresh towel goes down and six times out of ten she'll go and make another small deposit. ... Seconds invariably are sloppy.
And if she does at 4:30 am. no worries caterwaul until Dad gets up and cleans it - failure results in her urinating on the laundry tiled floor for it to soak into the grout!

My cat doesn't necessarily do that, but her little prissy butt will sit and watch me clean it, once I'm done she'll go investigate it to make sure it's spotless if it isn't she'll meow like her life is ending until I "double check my work" (don't get me started on forgetting to clorox wipe the floor around her box) that really pisses her off ???

Well, mustn't use a dirty toilet ya know!

That's your staff DUTIES slave. ...dogs have owners cats have staffing on bended knee

They always wait for clean sifted litter. ...clean it again and you'll hear them digging to take another piss 5 minutes later after you wash your hands and sit down for your favorite show

Wait for a clean box. . . yep