As the above poster mentioned, it does not do this. Hubitat communicates to the Hue bridge over the Hue HTTP(S) interface, entirely over your own LAN. Even in-app control on the Hue mobile app does this (or effectively the same using whatever interface the SDK exposes)--in fact, unless you sign up for and leave My Hue enabled, you don't get access from outside your own LAN at all.
So, the good news is you're good in that regard. 
My only concern with this was rate-limiting (e.g., if turning on a bunch of bulbs at the same time or using the "Start level change" and "stop level change" commands in Hubitat to begin and end the dimming of bulbs with button presses and releases, i.e., effectively dimming while held). The Hue docs recommend <10 commands/second to avoid this. I'm sure the real limit is higher, but in any case, I haven't noticed any problems with this. You also won't be able to use the Zigbee group broadcasts (something you can optionally do in the Groups and Scenes app), but that doesn't bother me (might be able to eliminate the "popcorn effect," but this is minimal for me with how fast everything generally happsn for me anyway).
