The control over the creature changes control immediately.
As the ability text on Dragonlord Silumgar states, the change of control effect ends as soon as you lose control of Silumgar, which also happens when Silumgar gets destroyed. A creature that changes control is removed from combat, which means, among others, that it will deal no more combat damage during that combat phase.
506.4. A permanent is removed from combat if it leaves the battlefield, if its controller changes, [..] A creature that’s removed from combat stops being an attacking, blocking, blocked, and/or unblocked creature. [..]