Theoretically, and isolated, it's easy to play a mode thinking of it as certain-degree scale derived from it's "parent" Major Scale. But I've found that when Aeolian (etc) is the tonic, I have to think of the intervallic construction of that scale (the Aeolian) rather than mixing it and thinking it's a sixth degree of another major scale, considering, therefore, two scales simultaneously.
In other words, if I'm playing (new) Milestones, I'm not thinking of the A Section chord (Gmin7) as the II of F Maj rather as a Gmin (Dorian) in and of itself. And so forth to other modes and tunes. I have to learn the intervallic structure of a mode in and of itself.
The above is, to be sure, a great way of learning the modes to begin with but, for me, that's where it ends.