My experience with the pocket chain saw was of it getting pinched in the wood fairly easily - mostly since its cutting on roughly three sides at once. One has to be very careful that the forth side (toward the uncut side) has to be where the pinch force is going to be applied. On a horizontal cut the blade needs to be on the top. On a vertical cut the branch needs to either be small - to minimize the pinch force - or sufficiently angled to move the pinch point to a "bottom" - somewhat like a horizontal cut.

I'd also suggest only using it on larger branches when you have two people available - just in case the saw gets pinched. You'll need one to lift the wood while the other frees the saw.