You were not in Michigan when the accident occurred, so the laws of Michigan will not apply to this accident.  In EVERY other state, property damage claims do not fall under no-fault.  Michigan is the only state that applies no fault to both injuries and property damage.  So yes, your insurance company will pay for 100% of the damage you caused to the other person's vehicle, up to the limits on the policy.  You will need to review your policy to see exactly how out-of-state claims are handled and what your liability limits are.  But auto accidents are governed according to the laws of the state where the accident occurred, regardless of where the parties actually live.

Obviously, you will also need to pay the ticket, but the ticket is not what makes you at fault.  You were at fault the moment you rear-ended the other driver, and you would have been responsible for the damages regardless of whether a police report was written.