A 556 timer is just two 555's in a single package. (I think you can get 4 in a package in a 558). Each are independent. So you would use one to create the 10 sec delay as a one-shot. Then use the output as the trigger for the second to create the 20msec delay. Then use the output of the second to trigger a 3rd for the second valve.
As discussed above, there are many, many ways to accomplish this. It all depends on what you are trying to "optimize". For example, you could just use one of the 555's as a 20msec clock. Then use other logic to switch the desired pulse to the right valve driver.
But, if the timing isn't overly critical and package count, etc. aren't critical, 555's are a straightforward way to go, and will interface pretty easily with your valve driver. They have a wide Supply Voltage range, so you can probably power them with the same supply as the valve driver (no need for separate 5Volt supply, etc.).
For my part, I'm partial to the CD4538 which is a dual timer, even easier to use than the 555, and cheaper.