On my type the mask do not drop down automatically if not above FL140 cabin altitude. Part of the drill is to pres the MAN PAX OXY = ON, but then again only if CAB ALT is higher than FL140, for confirmation of the automatic deployment.
This value is chosen to satisfy regulatory requirements for PAX O2 supply.
Thread drift: do you use headsets with OXY mask on? In a recent SIM session I was advised not to do it, which surprised me to a great extent.