* I am assuming that the tar paper is still on the home and that the shingling process has not begun.
1) I would demand that the roofer install new tar paper. This is your second line of defense and I would be adament about it. Remember, this is your home, not his/hers.
2) I would like for the decking to dry out, but with weather like it is, you really cannot take that chance. If you went without tarpaper for the decking to dry out and you had a storm, your insulation would ruin, your home interior would have leaks, you would be in a bigger mess. I would forgo the drying process. The attic and all should allow for drying to occur.
3) You need to have a heart to heart discussion with your roofer or the manager or owner of the company. If you are having problems now, then just change companies.
4) I have a thought about upsetting people working on your home. I feel that if you piss them off, they will take shortcuts and maybe not do the job that they normally do. Deal with the owner and have your discussions with them. The laborers out there are just workers in most cases.