Your adjudication?
Here's what the spell has to say for the conditions of the Alarm going off:
Once the spell effect is in place, it thereafter sounds a mental or audible alarm each time a creature of Tiny or larger size enters the warded area or touches it.
As long as they are outside of its area of effect when they Dispelled (and failed), the Alarm would not trigger. It only triggers when they enter or touch the area of effect.