Stiring up the yeast is only done when i move from my bucket to a airlocked carboy at about 10-17 days when the mead is still fermenting strongly but past the kraussen stage, typically 1.050 - 1.060 S.G.
IMO the last thing i want to do at this stage is remove active yeast population. If i use an oversized carboy instead of a bucket, I wouldn't rack untill week 6 or so. FWIW I've never experienced a stalled/stuck fermentation after my move from primary bucket to primary carboy because the yeast is still all there.
I could probably leave it in the bucket longer, but I feel beter getting it under an airlock while it is still expelling lots of CO2, this also allows me to start plotting the next batch if carboy's are empty.
The only reason I use a bucket is so i don't get krausen in/through the airlock.
Does this make sense now, when I make a fruit mead I do remove the Ingredient bag at this stage.
Anyway this is why i specificly used the word transfer instead of Rack, i don't consider it racking.
Edit:
Oh yeah, one last thing. The other purpose the stirring serves is that the main carboy and the top off (little) carboy have almost identical mixtures in them. While Topping off with water is fine I'm sure... I don't like the concept of watering down the must. This method Gives me extra must i need to replace the volume lost to the lees in an almost identical state of fermentation. (It doesn't kick off a new ferment like topping off with honey would.)