Jenkins pushing to branch overwrites commits made in interim
It really depends on your situation, but I'll go with the generic/naive approach and say do exactly what your developers do in the same situation: I pulled an hour ago, I made some changes, now I want to push my changes, but other changes have been pushed in the meantime. I commit, pull/rebase, then push. Assuming that whatever Jenkins is committing isn't tied to the commit it built from, this is the same process it should follow to get the same result.