Since the leak is liquid, the pressure in the steam side of the exchanger is basically constant until all the liquid inventory is gone. The time is the mass of water in the drum divided by the leak rate.
The API basis for a tube rupture is basically that the tube shears-off to give 2x the cross-section of the tube to depressure into- all of which will be seen as a steam load at the hot oil side PSV. This is obviously the highest design rate, but most tube leaks are not that extreme. Whatever you calculate for a minimum depressure time based on relief rate, it could easily take longer. Flashing of the water into steam, helped by the sensible heat of the hot oil may also reduce the rate, leading to a longer depressure time.
This is the way I see it from what you described. Others may have a different view.
best wishes,
sshep