Let me make this as simple to understand as possible. Stalkers have a drain magic trigger on their melee. It is an after damaging trigger. Rulebook says after damaging triggers are done before the model is removed. So that means the other player must discard a card before they remove their model. But for this to happen damage occurs, therefore searing mark is applied.
So if in good conscious you can tell me the stalker does not apply burning before the model is removed then Idk.