I didn’t recognize when exactly, but after some update conditional logic was broken.
Now I have installed ACF 5.6.1 and conditional logic seems doesn’t work (or at least doesn’t work in some cases).
It was worked before, but now when I set up to show a particular field for certain values of another field, this particular field is never displayed (for any values of the second field). If I set up to show a particular field when the value of another field is not equal to some given value, then my particular field is always displayed (also for any values of the second field).
An interesting detail: sometimes (in rare cases) conditional logic still works. But in most cases in exactly the same situation (exactly with the same fields) it does not work.
P.S.: I do not have any tabs for these specific fields.