It's important to note that by this point in the conflict, the Separatist armies are losing what little ground they managed to gain at the start of the war and that the Separatist leadership is on the run, fearful of the same sort of "decapitation" strike they tried against Palpatine if they go and hide on one of their own planets. Sidious, however is still promising them that if they follow his orders, they're in line for victory (via a settled peace) and will receive a "great reward".
NUTE GUNRAY: The war is over. Lord Sidious promised us peace... we only want...
Revenge of the Sith Script
When the Separatist leadership hear about the Jedi being removed from power (following what appears to be a failed coup attempt) this must seem like manna from Heaven for them. They order their own droid troops to disengage, presumably on the basis that now that the Republic forces are lacking any leadership-class troops, Chancellor Palpatine will finally be forced to come to the negotiating table and will have to allow the Separatists to keep the planets they've annexed.
Clones open fire, and Jedi die.
All across the galaxy. All at once.
Jedi die.
Order Sixty-Six is the climax of the Clone Wars.
Not the end-the Clone Wars will end some few hours from now, when a coded signal, sent by Nute Gunray from the secret Separatist bunker on Mustafar, deactivates every combat droid in the galaxy at once-but the climax.
It’s not a thrilling climax; it’s not the culmination of an epic struggle. Just the opposite, in fact. The Clone Wars were never an epic struggle. They were never intended to be.
What is happening right now is why the Clone Wars were fought in the first place. It is their reason for existence.
Star Wars: Revenge of the Sith - Novelisation
In the film it's a bit more muddled, with Vader sending the signal to shut down. This is clarified by the novels which state unequivocally that the signal had already been send for the droid armies to disengage from fighting. Vader then sends a signal to the Trade Federation to shut down their droids permanently.
DARTH SIDIOUS: Send a message to the ships of the Trade Federation. Tell them the Separatist leaders have been wiped out.
Grievous and Dooku have been destroyed. All droid units must shut down
immediately.
Revenge of the Sith Script