Either turn in on in both apps or turn it off in both.
Actually, I notified you DO NOT linearise your working space until you fully understand linear workflow. That, among other things, means you shouldn't linearise working space in all AE projects. Quite contrary, you should understand, when to linearise them and when not. That Stu Maschwitz blogpost, the link to which I submitted, contains a lot of other links, including this one to the discussion on when to go linear.
Your current issue relates to the question that neither PrPro nor AME is colour manageable (color aware) application. It can be corrected in several ways:
1. As Rick said, just turn Linearize Working Space off (it can ruin your current colour correction as well).
2. Apply Gamma Correction effect onto your dynamically linked comp in PrPro timeline (which is not quite correct workaround, actually).
3. So as not to rebuild Dynamic Link, pre-compose what is in your dynamically linked comp now into another one. In your modified dynamically linked comp go to View menu and disable Use Display Color Management. Apply Color Profile Converter onto your pre-comp layer and set Output Profile to sRGB, leaving Input one in default 'Project Working Space' mode.
Thanks Fuzzy.. I know I have lots to learn about color management, so thanks for being patient and providing this information.