ESPN announcers made a solid point though. Yes, Correa was out of the baseline, but the pitchers job is to just hit the player with the ball and it's an out. Obviously we'd be mad the other way around, but we'll see what happens the rest of the way through.
It doesn't matter unless it affects the play, it didn't. The bad throw was on the pitcher and wasn't due to where he was running. Had he thrown the ball towards first base and it hit him due to where he was running, it would have been interference and he'd have been out. The pitcher just had a really bad throw.
According to the rules, the manager has to notify the umpire that he will be protesting the game before the immediate next at-bat. If the team wins the protest with the MLB office, the game will be replayed beginning immediately from the protest spot (same inning, players, etc.).