What triggers the IS motor?

I've recently changed up my bodies' configurations so that half-press shutter speed doesn't AF, and I have to use the AF-ON button on the rear of the body (thumb) to AF.

That said, what action spins up the IS motor on a lens? Is it tied to the AF action? Or is it always tied to the half-press shutter action?

AFAIK, it's tied into the shutter button. You can AF with the AF-ON button without cueing the IS motor. Alternatively, you can cue the IS motor without focusing with pressing the shutter button.

In that situation, be sure to remember that IS usually needs a moment to fully kick in, so if the exposure is fairly long, you will want to wait for the motors to fully spin up and do their job before you take the shot.

most Canon IS motors kick in within a split second. my 28-135 was very quick.

My AF button, along with the 1/2 shutter spins up the IS.