They are both closed-source, so you won't get to see how Hubitat did it (though you could look at CoCoHue for one example of how the former can be done). However, I'm not sure either of those would be particularly helpful in your case--the Lutron app relies on telnet, not HTTP (which I assume your devices use), and any Hue integration is one-way (where Hubitat polls the devices; the Bridge/devices do not send state directly back to Hubitat).
What it sounds like you might want is a local (or cloud) OAuth endpoint that your devices can POST (or PUT or GET) a message to. If you already have something working like this on SmartThings, it's nearly identical except that Hubitat also offers local endpoints (which I'd prefer). You do create these by defining mappings in an app (and making sure you've enabled OAuth on it). Here is a simple example: Hosting an HTML endpoint (though this is only a GET and it's used to return an HTML page here but could be used with a bit less work to just return JSON). In your case, you'd probably want mappings that accept data from a device, maybe using POST or PUT, but the general idea is similar. I do have some examples of this, but it's from a new project I'm working on that I haven't shared widely. There may be good examples out there somewhere...
I should also mention that you might be able to use MakerAPI and avoid writing your own code at all (it can be configured to accept a POST at a specific URL for any specified device), at least on the Hubitat side.
