Currently there is nothing that can benefit from the SS-HSF having a face-up disrupted counter between the casualty phase and the beginning of the SS-HSF player’s movement phase, so it doesn’t matter as much as the SS-HSF ignores it so can defencive-fire, etc, still.
However, I usually leave it on anyway then remove it at the beginning of my movement phase like your supposed to since that is the rule; and who knows in future sets there might be something that can effect it.
And really, it’s not like it’s a lot of effort either way.