I would consider updating to an Edge Driver. Otherwise what you end up coming up with for the Groovy driver might be short-lived as SmartThings is in the process of shutting down Groovy.
One of the challenges with Groovy DTHs, is they sometimes show all of the possible options for a capability even if the device doesn’t actually implement those options, so it’s a bit hard to say if those are actually valid options. That’s why I was suggesting the trick around setting up all the different trigger values (more on that below).
Just to reiterate this point, I’m not intimately familiar with WebCoRE, but I believe the example you showed uses the Extra Event Data I mentioned here. Doing the trigger test should help us better understand what’s happening when the device is single tapped or double-tapped so we can setup the rule accordingly (next section)
I meant something like the following…
In the triggers section, I have a trigger for ‘button changes to pushed’ and another that is the inverse of that with ‘button changes and is not pushed’. That effectively captures all of the potential trigger scenarios of the button attribute.
The idea being that we can then try pushing a button and then review the Rule Logs to see what value triggered the rule when the button was either pressed once and when it was pressed twice. That will clue us in to the best way to configure the rule.