What happens after killing the Stalker on warframe
This was not a Stalker attack, but by a death squad from one of the Syndicates. These death squads have nothing to do with the Stalker and they also do not drop Stalker loot.
You get targeted by death squads when you have negative standing with them.
Regarding if anything special happens if you manage to instantly kill the Stalker: No
There is (as of yet) no special reward if you kill him quick.