Interesting. I've never had that happen when paper piecing. Unfortunately, not familiar with your machine and/or it's settings so no clue if that is part of the problem. I normally use copy paper for my paper piecing so not sure if that may be the culprit or not, although I know many folks use the newsprint weight paper and not aware any of them have the issues you are.
I'm sure someone else will be along to help shortly.