Bug with Color per Mode on linked Hue bulb

FYI, the Hue Bridge connection goes over your LAN, not the cloud.

I think I've seen problems with RGB(W) bulbs and Hub Link/Link to Hub before. I did a search and found someone who had what sounds like a similar problem and someone else who was able to replicate it: Control Hue RGB lights through a linked hub - #25 by csteele

If you're able to set up HubConnect instead of Hub Link/Link to Hub, you'll likely have much better luck. It's third-party code, but staff have recommended it to users in the past, so it should be pretty solid (just a bit more difficult to set up). Hub Link/Link to Hub haven't seen many changes--actually none that I can think of--since Hub Link was introduced (the original was just Link to Hub for connecting to SmartThings, and the latter was added per customer requests). I'm guessing their interest has waned since the advent of HubConnect, though this does seem like a bug they could fix.

That being said, you could also just integrate your Hue Bridge to both hubs if that's all you need the lights for. Hub Link/Link to Hub, HubConnect, and the Hue Bridge Integration are all (unless you use ST for the first or second or specify otherwise for the second) LAN integrations, so I'm not sure I see much advantage to segregation there.