Brownlab,
What kind of 'major incident'?
For certain medical incidents, the dispatcher will start a time clock so the medics will have an idea of how long they have been working. The longer it takes to stabilize a victim, the less chance they have to survive or fully recover.
I've also heard time clocks for multi alarm fires so the on scene commanders have an idea on how long it takes to control.
A time clock may also be an indicator for move ups or recalls. If you take a large number of units from a geographic area, especially for a protracted period, it leaves that area basically unprotected. All departments have some kind of redistribution plan to provide coverage (somewhat reduced) for their entire service area.
However, mainly the time clock seems to be for severe medic responses (like a seriously injured accident victim, trapped in their car).
Fairfax County may have other reasons, but these are fairly common.