Sounds like you have the system responding far too quickly because your proportional gain is far too high for the characteristics of the valve
Have you tried ziegler-nichols loop tuning? It gives a good starting point from which you can then fine tune the loop.
We have valves that operate at around 25% to 30% for flow control and it works perfectly. We deliberately chose an over-damped response as our system is chemically very sensititive to sudden flow changes.
You'll need to check the flow characteristics of the exact valve you've installed but for a generic butterfly valve you're flow is relative to the position so you're operating at 10-20% of flow so sounds like you've oversized the valves.
To be honest, I would start with a low proportional gain and a little integral to get an overdamped response. You'll need to check the speicific set-up for the PID controller as a lower I setting usually means a higher frequency of intgrating the error and therefore a faster response, so you might want to set the I setting higher.
Once you have an overdamped response you can start increasing the P to speed up the initial response (but if you're operating at the lower end of the valve then I'd probably keep the P value low). I'd then start decreasing the I to increase the valve response. But again there are so many factors to take into account, such as the dead-time response, that it's hard to give specifics.
I would also look at the equation for the PID controller you have as well as that will give you an idea of how it will respond.