Most likely, as soon as the judge signs the order. Most motions have either a hearing date (where the parties can appear and discuss the motion) or a submission date, (where the judge will consider the motion without the parties appearing in court).
I'm not familiar with this particular motion/procedure. However, I can tell you that a motion does not "take effect." Rather, a motion is a request that the court take some action. A court can hold a hearing on a motion, rule from the bench to grant or deny a motion, issue a written opinion on a motion at a later date, or even take a motion under advisement without any indication when the motion will be decided. Accordingly, only the court can say for certain if and when a requested relief will be granted. This particular request seems to be for withdrawal of a motion to set aside (or dismiss) that was already pending in front of the court. In Michigan, the party that filed the motion (you in your case) would normally just contact the court to withdraw the motion, and this would happen immediately.
THE RESPONSE ABOVE IS BASED ON THE FACTS AND REPRESENTATIONS MADE IN THE QUESTION TO WHICH IT IS DIRECTED. THE ABOVE IS ONLY MY EDUCATED OPINION ON THE SUBJECT MATTER, AS A LICENSED ATTORNEY IN THE STATE OF MICHIGAN. IT IS NOT LEGAL ADVICE, AND THEREFORE SHOULD NOT BE CONSIDERED AS SUCH. NOTHING IN THIS RESPONSE FORMS ANY TYPE OF ATTORNEY-CLIENT RELATIONSHIP. YOU SHOULD NOT RELY ON WHAT IS STATED ABOVE IN TAKING OR FOREGOING ANY ACTION.