Ohio is part of the Drivers License Compact, while Michigan is not as you stated. Though Michigan is not part of this agreement to exchange moving violation information between state courts and DMVs, they still have their own agreements to report this information to other states and also get notified if a driver licensed in Michigan is convicted of a ticket out of state.

The MI Department of the State notes that if an out of state violation corresponds to a violation listed in Michigan law, than the conviction will be posted to your driving record and points will be assigned as required by the MI Vehicle Code.

From this information, it would appear that not only will the Ohio speeding ticket be placed on your Michigan driver's license but also be assigned 2, 3 or 4 Michigan DMV points. The amount of points will depend upon your rate of speed over the Ohio speed limit that you are convicted of going.

There are only a few states like MI that are not part of the DLC but most all of them still receive information on their licensed drivers out of state moving violation convictions and share these types of convictions back with a motorist's home state as well.