We had this discussion indepth very recently. The conclusion was that the timeline you are refering to is EU, and that Star Wars, being intentionally an idealistic, fake, imaginary, fairy tale like setting, it is more than reasonable that the Empire crumbled instantaniously once their super weapon and leader had been lost. Also, apparently, 1980's EU supports the idea that the entire Galactic Empire came to an end the instant a singular man (their Emperor) was killed. If only the Rebels had known it worked like that, they could have sent several agents to infiltrate the Imperial City and take whatever actions necessary to kill Palpatine.

Rebel Agent one: Alright, jobs done. The Emperor is dead. I poisoned his steak, lol.

Rebel Agent two: Whooohoo! Job well done.

Rebel Agent one: Oh f***ing hell! Stormtroopers! We're so f***ed! What are we going to do?

Rebel Agent two: I don't know, looks like this is the end, pal. It has been a pleasure working with you...

Stormtrooper Squad Commander: Hold it right there Rebel scum!

Stormtrooper Cadet: Look sir! The Emperor!

Stormtrooper Medic: We're too late. He's dead.

Stormtrooper Squad Commander: Dammit! (drops gun, rips off helmet and throw it in anger, kicks gun across room) Dammit! Dammit! Dammit! Dammit! It's over! It's all over! We failed! We failed the Emperor! We failed the Empire! We failed the dream of unity, hardship, and war throughout the galaxy! May our children forgive us. Dammit! (Angrily walks out the door in defeat, peeling off his armor and throwing it in anger, piece by piece. Slowing, an entire squad of disheartened Stormtroopers begin taking off their own armor, revealing heart broken faces as they slowly turn and walk away from their fallen leader.)

Rebel agent one: What... the... f***?!