No, Promotions only run on completed builds. If you want to run it in the middle of the job, then it's a build step, not a promotion. You can either configure build steps for your actions (same actions as promotions). You can even call other jobs, and wait for them...
You probably have a post-commit hook that is triggering the same job through a URL or jenkins-cli Edit after OP comments: But I start to wonder on the deploy-job, I didnt configure "Build when a change is pushed to Github", instead, I use "Build when another project is promoted", so...