It's not that you/they can't communicate across the barrier, but rather that you/they can only communicate in very specific well-defined ways: in this instance, the Hub only communicates with local-network devices via HTTP, and only when the local device initiates the conversation. The Hub can also communicate with a few IP addresses at Philips, if you allow it to "phone home"*. This can be written as a couple ACLs in the router that say "(Hub IP address) can only send HTTP traffic to local network, and only if the other end initiates the conversation", and "(Hub IP address) can send/receive to/from (IP addresses in Philip's domain)".Or is the entire idea that you can’t communicate across that barrier?
As far as your original mention of WiFi - it's useful in terms of understanding networking, but doesn't come into play here, because the Hue bulbs talk ZigBee (only) to the Hub, and the Hub (only) speaks ethernet to your home network.
As an aside, the Hub is controlled by the official Hue app - and all the unofficial Hue-related apps (there are many) as well as by HomeKit, and Alexa, and probably your SmartRefrigerator - via a fairly straightforward RESTful interface over HTTP, using JSON. It's quite simple to write scripts that interact with the Hub and turn lights on/off, collect status, and such. (I've got a bunch of python scripts I use for setting up specific scenes and such - and my own custom home weather station has a touchpanel with one column reserved for buttons to select various scenes.) Anyway, if you know how to program, and wish you could make your Hue lights do some particular thing - you probably can. Their developer program is free and provides complete documentation of the interface.
*: Having the Hub "phone home" to Philips is there to allow remote (away from home) control of your lights directly from the Hue app on your phone/tablet. This is from before HomeKit (and its own flavor of remote control) was a thing. You don't really need two such methods active, and HomeKit works with any other IoT devices you have (rather than only Hue devices). So I have the remote access in the Hue app turned off, and control them remotely solely with Apple's Home app (have an Apple TV at home, which handles HomeKit command traffic between Apple and my home). I trust Apple's security more than I do Hue's.
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Nice to see someone who speaks network around these parts.The main issue is that Apple/Homekit rely heavily on Bonjour (mDNS) for device discovery. But mDNS normally only works within a subnet since it uses broadcasting. However, you can set up an mDNS reflector to enable mDNS across subnets. One implementation is Avahi (which can be used on Linux-based routers such as pfSense).