Do you let the turntable spin when putting down record and attach the clamp.

No, the platter is stopped when putting on or taking off a record. When the clamp is attached, the platter is turned slowly to make sure the clamp is tightened correctly. After playing a record, the arm is moved to the safe position, and the clamp is removed as the platter spins down.

I try to help the platter start up by gently spinning the platter.  I use reduced voltage to operate the table and it won't start at that low voltage without some help.  I use a Variostat to manage the voltage for ~ 70v operation (VPI motor). 

The power is aways on.
One cannot fasten a reflex clamp without stopping the rotation.
Reset AT pickup, place record, place clamp, brush diamond with Stylast. Give clamp a spin (to save the belt from dead start on a heavy platter), hit the on swittch and drop.
Rinse and repeat.

If your turntable is delt-drive you can damage it this way.

If it’s Direct Drive you can’t damage it, and you can change record and add/remove disc stabilizer on top of the record on the fly (with spinning platter if you like).

I press the stop button each time I change record. I put my disc stabilizer on the spinning platter (after I turn it on, not before). But I use ONLY direct drive turntables.

I don't think I want to attempt putting the periphery ring clamp on my VPI while it's spinning. With my direct drive turntables, I leave the power on but stop the platter from spinning when I change records.

Platter is always spinning for the session. No clamps or weights.