Once after you save your last puffle (could be any puffle) Gary will message you:
If you can't read it Gary said:
"SUPERB! With all 10 chips, you can disable Herbert's mind control antennae. Just place the chips un the corresponding slots on the machine.
Be careful,he'll be on alert!"
So you go to the same place you saved the white puffles in, and Herbert will trap you! So you go through the vent.
And you will go through the room for the vent and once you come back in Herbert's base press on the machine that has the puffle on it. Once you press it you would see the puffle chips scattered on the screen
As you read you need to place the color chips in their proper spots. I'm not going to tell the rest of the mission, but I'm going to show once you the prizes once you finish the mission.