Thanks again.
About "clean, no chalk surface" - this exactly is the problem. The paint on EPDM roof is aging from the day one, leaving chalk-ish powder on the surface that can be picked up with any wet or even dry rag. Solvent just dissolves more paint, after removing most of chalk - and also removes oil-ish residues, if there are any.
My roof had this chalk of course. Everybody I asked, had same calk on the roof. I felt that this caulk would affect the adhesion of sealant, and tried to remove it very thoroughly - water with a drop of dishwashing liquid, then lots of clean water, then solvents. Cleaned areas became very smooth after this, and spider-like web pattern emerged - this is black rubber starting to show from under white paint.
And, no matter how many times I rubbed it with clean water after soapy water - the rag still picked up some traces of white stuff. The ultimate test was packing tape - when it didn't pick up anything white, I considered the surface clean.