Doesn’t that contradict the US constitution though, WRT presumed innocence?
No. Self defense is an affirmative defense to a charge of murder. The trick is to get prosecutors to not charge people who have used deadly force with justification. Some prosecutors drag people through the mud to score political points - see prosecution of George Zimmerman. One way to correct this is to jigger the burdens of proof.
Ohio has the WORST self-defense arrangement in law. Burden is on defendant to prove it. Not so elsewhere, where generally it is up to the prosecutor to disprove it, beyond a reasonable doubt.