Just think of the same concept as Fasst Co Flex bars. Same thing but built into the fork. Unfortunately, unlike the Flex Bars you cannot get different elastomers to dial in stiffness.
Having had those bars and run them for a while, I don't think buttercups come even close to the benefit those bars provide. Those bars are the only thing that completely eliminated hand fatigue and pain for me, but I doubt they mitigate vibration much especially given how much friction is in the pivots and how firm the elastomers are. They do a great job of absorbing larger impacts that would otherwise go to your hands, though. There are trails I completed without stopping due to hand pain for the first time in 5 years after putting those bars on, but running a Lyrik Ultimate...not the same outcome or result.
Most reviews also complained about small bump sensitivity and increased fatigue compared to earlier models, something I would've thought buttercups would help with if the marketing is to be believed. I didn't have issues with small bump sensitivity yet (time will tell), but I can say the level of hand fatigue I had was on par with or slightly more than other forks I've run. That's subject to many factors and I need more time to really conclude how it does, but I don't think it comes close to comparing to the Fasst bars and I am not convinced I see much of an improvement over other forks I've used. It might be better than if they weren't in place on the same fork, though, but the only way to verify would be to replace them with a metal insert.
I found the fork better than I expected based on reviews, maybe buttercups are part of that, I'm just skeptical unless it's solving some other problem specific to their forks that isn't evident until they are removed. I've ridden several new forks in the last few weeks that didn't have them and were comparable (or even better) in feel.