When does the overspeed alarm goes off in a plane?
The overspeed goes off when either the indicated airspeed exceeds that limit or the mach speed exceeds the mach limit. At least that's how it worked on 747-100/200 aircraft.

The 350 knot figure for the max operating airspeed sounds reasonable to me as long as you're low. From memory that was around the max operating INDICATED airspeed for 747-100/200 aircraft. Remember, though, that indicated airspeed decreases with air density. A 747 cruising above 30,000 feet at around 550 knots TRUE airspeed is going to show an indicated airspeed of less than 300 knots. However, that cruising true airspeed of 550 knots or so is going to be around mach 0.86. The max mach number for the 747 was 0.92.

If you were at, say, 15,000 feet and speeded up to 350 knots, the mach number would be much less than 0.86.

Take your sim up to 35,000 and see what you get.