You know how it’s like an instinct for wolves to protect their mate?
They don’t even think about it, it just comes to them naturally. Their mate is caught in a dangerous situation or is going to be in a dangerous situation and they’re ready to defend them.
It’s sort of like this scene.
Derek caught sight of Stiles getting ready to do something risky, something that posed a threat to his safety and he immediately came chasing after Stiles, trying to get him to stop and ready to protect him if anything were to go wrong.