or is the stack of orbs as a whole on a timer?
This one. You can build stacks pretty fast with Thunderstorm and shock conduction 2 but volatility has a cap on gaining stacks so you can't gain more than 10 a second.
I don't remember for sure but I believe the popped volatility (volatile power) doesn't get refreshed on gaining more stacks.
If you're playing chonk though you're better off going for into the breach plus lucid dreaming and speccing purple flames if you stack remnant pick up range you'll get a consistent 6+ purple flames which can be 80%+ gain as extra chaos damage.