OK, I have no idea how the primer could possibly be detonated by using an inertia bullet puller.
However, I do know something about cartridges being fired ouside of a rifle. In the good (bad?) old days it was very common to set a loaded cartridge on a stove, in such places as a hunting camp, or some other place where men were isolated for considerable periods of time, living in some remote cabin and just ran out of other sorts of amuzement.
So, from the horses mouth, here is the skinny on it. A loaded cartridge sitting on a hot stove will, in something up to half a minute or so, depending on how hot the stove is, will detonate the primer. And when the primer goes off it ignites the powder. The rifle case, be they 30-30, 303 or 30-06, usually didn't ruptre, and at this late stage, I can't say for sure if any did or not, but I don't think so. The bullet would fly out, hit the roof of the cabin and go bouncing off somewhere. To be safe, the people doing this would be on the bed, which in the type of cabins I refer to, would be only maybe 8 feet from the stove, and but a blanket between them and the stove. The bullets would barely make a mark in the board roof of the cabin. Usually not visible of where it hit.
And a bit of a surprise, 22 long rifle would go off nearly as loud as a 30-06 and pieces of the case would fly around the room.