Yeah, that's exactly what the Auto Mode is for. You can assign a specific Preset Mode to any application.
Open the Dell Display Manager interface and go to the Auto Mode tab. The software is pre-configured for many popular apps. To add Photoshop (or any app), just drag its icon from your desktop or Start Menu and drop it into the current task list. Then, assign it the Preset Mode you want (like a color-accurate mode for Photoshop).
If that didn't work: Make sure Auto Mode itself is enabled in the DDM settings. Also, note that DDM cannot assign preset modes to non-executable files like ZIP archives or scripts.
Heads up: The assigned Preset Mode can be the same on every connected monitor, or it can be different for each one. When you activate Photoshop, DDM will switch to your chosen mode automatically.