When is Minimum Safe Altitude Warning triggered?
The system projects the altitude that an aircraft will be at based on recent track and a calibrated "look ahead time" and an expected controller response time.  That value is then compared to a calibrated altitude floor.  If the aircraft is projected to be below the floor, then the controller will be alerted.

The specific values for all those things are calculated to minimize false alarms, accommodate the type of operation and local operational needs.  The values are specific to that facility and that area and so a straight answer isn't exactly possible.

Here are a few interesting resources in case they help.
Minimum Safe Altitude Warning
EUROCONTROL MSAW Guide