Your suspicions are close in terms of your issue nature, which resides in colour management, but rather the opposite to what happens in your case. If you set 'None', AE doesn't assign any colour profile to your footages, it simply copies data from the source and transfers them to display, where your 'huey D65 G2.5 A0.00' profile is taken into account, whereas your media player is most likely interprets your ProRes file as Rec.709. If you reimport it into AE, you'll probably see no difference between your composition and exported ProRes.
So as to fix your issue in principle you need to establish proper colour management workflow: set your working space to Rec.709 and assign Rec.709 colour profile on exporting (in general case you should define where you're going to deliver and then set appropriate working space, such as sRGB, Rec.709, DCI etc.).
Thanks Fuzzy, that is exactly what was happening. When I imported the video back into After Effects, the videos were identical.