I do not have any Philips Hue Dimmer Switches... However, maybe I can offer some troubleshooting advice.
Step 1: For now, please ignore the Button Controller 5.1 rule. Instead, please open the Device Details page for the Hue Dimmer Switch. Watch the Attribute values for Pushed, Held, and Released on the web page, while you perform those functions on each of the physical Hue Dimmer Switch's buttons. Do they all register properly? If so, move on to step 2 below.
Step 2: Now, open the device details page for your LED Bulb. Use the "Start Level Change" and "Stop Level Change" commands, for both UP and DOWN, and monitor the bulb to see if it reacts correctly or not. If the bulb is behaving as expected, move on to step 3. (Just re-read your post, and it looks like you've already tested this. Nice!)
Step 3: If both physical devices are performing as expected, per the tests above, then we can safely assume there is an issue with the automation (i.e. the Button Controller 5.1 rule.) Delete the Button Controller rule, and try recreating it to see if it then starts working. Or, try building it using a different app, like Rule Machine.
Personally, I really like the community Advanced Button Controller (ABC) App. I use it with Lutron Pico remotes all over my house to accomplish exactly what you're trying to do.
Good luck and let us know how it goes!
