The paint tool works on the actual layer, as a result motion tracking applies after the paint tool, so your burn mark will move around. (I think)
There are a couple of ways around this:
You could either pre-compose your footage and apply motion stablisation inside the pre-comp, then re-wobble it later – see Andrew Kramer’s demon face tutorial for the best way to do that.
The alternative is to create a new layer, apply the motion track data to that layer and use Vector Paint and transfer modes to add the burn mark.
Graham