Michigan is not part of the Drivers License Compact, which allows most US states to exchange information regarding moving violations. The Michigan Department of State though requests other states to report back citation convictions so that if an in-state violation corresponds to the out of state offense, actions can be taken.
Michigan law mandates that the same action be taken for tickets received out of state as those received in MI. Because of this law, points and license suspensions may be imposed as well as the violation being recorded on your MI driving record. To find out if points will be assessed and if so how many, check with the MI Department of State.
Having a 3rd moving violation on your Michigan driving record within 3 years is likely to cause your insurance rates to rise. It will depend on insurance companies rating system though so check with them or the Michigan Financial and Insurance Services with whom insurers must file their rates with.