That makes sense now. The entire roof is dependant on the tar paper itself and how well its nailed on. Obviously the membrane has no attaching quality to the decking, and if the tiles are foamed down then the same as well. So cutting strips would be a bad idea.
Was the felt 30 or 42 pound ? I put a granulated torch down on part of my roof down there many years ago. IT was all dependant on how well the underlayment was put on and how well the edges were adheared to the drip edge. The cool thing about that stuff is if you ever get a damaged spot, you just fix it with a soldering torch.