I agree with RissiaSunbeam1918, if Michael became Tsar after Alexei then he was the Tsar (Michael)
I'm not sure how the Law worked by that time, but today a person who hasn't got the majority of age, is under his or her parents legal authority, which means that in any legal or political desicion that must be taken in benefit of the child, it must be done by the parents, so if we apply this to fact the Tsar abdicated for him and his son, then that would had been legally right.