How to deal with different color space for the same project ?

I've been working lately on a very long motion design video. For more reactivity, i've been exporting the whole in AME, and some short adjustments were exported in After effects. But, when the editor (FCP) wants to replace some parts, a color shift is noticable on the background. 

I specified an sRGB color profile in my AE Project settings, but still I've been struggling to understand how to fix the color shift between the two, as AME seems to put color profile to Rec709. 

I would like to know if there's a best practice for that ? as some tight deadlines require to export through different softwares.