Both the feds and the states are prohibited from creating ex post facto law.
Adding to someone’s punishment post-conviction is explicitly ex post facto.
This is why Ohio reasons that this particular person should not have to register. They understand the constitution, and their registration law is constructed to obey it.
However, the supreme court has ruled that registration is “not punishment” (which is sophist, ridiculous and absurd, but regardless, that’s what they said.)
Consequently, any state or the feds can register anyone, for anything, pre- or post-conviction, guilty or not. Another example of just this kind of misuse of power is the no-fly list. They make the list, decide you belong on it, bingo, you’re on it, and you have no recourse.