The Hue integration has always relied on polling (new firmware just enabled a configurable polling interval). The communication is only "bidirectional" by brute force--changes made on the Hue network rather than through Hubitat will take until the next poll/sync on the Hubitat side to register.
The Hue integration in Hubitat is presumably there because people want to control Hue devices from Hubitat, and since the Hue Dimmer is basically just a button device that just sends events and can't really receive commands, I understand why it's not supported. Even if it were supported through the integration, there would be considerable delay (the next poll time) between pressing the button and Hubitat figuring out it was pressed by parsing the JSON it receives from the Bridge and determining if the "last press" time is newer than the last one it knew about. (I think I've seen some ST integrations that work like this.) Pairing it directly to Hubitat is probably the best option if you want to use it this way; I've tried it that way before but like its behavior on Hue better, so I moved it back and didn't really use it on Hubitat long enough to see if I had problems.
SmartHomePrimer was correct with what I meant--I assume you had the Dimmer paired to Hubitat. I forgot about the channel idea, which isn't a bad thing to check if you can since it sounds like a weak network is probably not the issue.
As for the name of the driver, I'm assuming they just happened to choose "Hue" for one and "Philips" for the other. If you pair it now (as opposed to moving over from a custom driver you needed on old firmware), it should find it automatically so you don't need to worry, and the "hueBridge" drivers are ones you shouldn't ever have to manually choose. If you ask them nicely, they might change the name of the dimmer driver to match alphabetically.