AE color management don't work with "video out".
When working with a second monitor or blackmagic video output you just get "none" in color profile. This is a BIG problem.
As a quick solution is just put a option in preference to use same color display as the selected "primary viewer".
The best solution would add the color profile option in the "video preview" under each of your output devices. By doing that, you will have the option of monitoring diffent color profiles at the same time.