I agree with @cmason1957, the kieselsol and chitosan must be well distributed, and as long as that happens, it doesn't matter how.
I use a drill-mounted stirring rod, which I highly recommend. When making a kit I typically degas by stirring for 2 to 3 minutes, changing direction every 30 seconds. Then add the kieselsol and stir for another 15-20 seconds. With the rod it's going to be fairly vigorous, although the wine is still moving from the degassing.
The addition of the chitosan has changed. Older kits said to wait as little as 1 minute, while some now state 24 hours. I put the towel back over the fermenter and let it set for, at most, an hour. Stir in the chitosan (30 seconds with the drill mounted rod), and rack back into the carboy.
The wine will be expelling CO2 for days -- stirring kicks the degassing process into high gear -- so the wine is fine for the hour.
Honestly, I could put the chitosan into the empty carboy and rack the wine back in, that will distribute it well enough. However, I stir it in anyway.