Hi Keidrych - Photon's color science is designed to work on images in RGB color spaces. It currently works best on sRGB images or REC.709 videos. If you intend to use it in an ACES project in Resolve, the suggested workflow would be to add an ACES Transform node (ACEScct to Rec.709) before the Photon Connector node and another one after (Rec.709 to ACEScct).
As for the external monitor: The color editing you do in Photon is transferred back to Resolve each time you either play back the clip in Resolve our press the "Render" Button that is part of the Photon Connector Settings. That's when the edited image shows up on the external monitor as well. The color edit won't get applied constantly in Resolve as we currently have no way to trigger Resolve and make it pick up the external changes (We talked to the people at Blackmagic though and hopefully they will give us this option soon). We noticed in our test setup with a Tangent Wave 2 panel that Resolve can be triggered by pressing the Stop-Button on the panel as well.