So, the problem seems to run even deeper and is unrelated to expressions.
Apparently, if I nest several copies of the same 3D comp with collapsed transformations, then the very top layer influences the rest of the copies, e.g. changing its time value (animated timeRemap, expression, or simply shifting the layer over time), makes all the underlying layers within the 3D container, look as the top one.
From there, all what I experienced earlier.
Am I missing anything essential about collapse transformations + time attribute? Such behavior seems fundamentally abnormal, however it should be tested by the other users, as it might be a local glitch.
Here I add a AEP file made of solids alone, see yourself by shifting the “MOVE ME” layer on timeline back and forth. You can also try enabling randomization expressions in *T, *S, *E compositions, which will override the existing color animation and make it more obvious.
Please, report back if you experience similar behavior.