Simple, really: You are using a) a wrong color space b) your system is not calibrated, but you have color management enabled and c) use formats that don't support color management. This is simply wrong from stem to stern, especially with regards to b) and c). Why would you even use Adobe RGB when video works on Rec 709 or even more generic sRGB? I think you do not even understand the point of CM on a fundamental level. you don't dictate the color space by your source files, you simply import them into your working color space - regardless of whatever it is set to. The color metrics engine will apply any corrections necessary based on the associated/ embedded profiles, which ultimately is the whole point. Conversely, enabling CM for output will require a format that actually uses those corrections, which comes down to only a handful. so to cut a long story short: Unless you are willing and technically able to establish a proper CM workflow simply leave it off and just use the default sRGB that AE ever has used.
Thank you for you're explanations.
You're right, I don't know much about color management and formats . And it's the first time I tried to use a color space. I now understand, that I shouldn't use an output color space and I would like to don't use one for the project, but the reason I used one was, that the colors in the project allready looked washed-out with the default setting "none". But when I changed it to a color space like for example RGB they looked right, like in the original footage...
And how can I calibrate my system?