Currently, it should update every time you select a procedure in the MCDU. The choice is further dependent on your current 'Phase of Flight', such that in and before CLB phase, it will prioritize tuning the departure runways ILS for SRS/RWY. It will not auto-tune to the arrival runway's ILS until you select an approach procedure, and you are in CRZ (or beyond) phases of flight.
It's not true. I select the approach during CRZ and the ILS frequency are ALWAYS wrong. I have to update it in the NAV/RAD page with the correct ID of the chosen ILS. So it's true that it tunes something, but what it tunes is a wrong ID.