Rampage start either Trial by Fire or Uzi Money. When you complete the objective, the mission and the rampage will both pass (as long as the rampage didn't fail before the mission objective timer starts). The counter for the rampages doesn't increase, but completing all other rampages gives you the percentage (with a 18 or 19 out of 20 counter).

In addition to this, it can be used along a remote item pickup to skip the drive to and from the flamethrower in Trial by Fire, as can be seen in

Note: If the mission fails, the rampage also fails. Note: Simply picking up the flamethrower remotely doesn't spawn any triads in Hepburn Heights. The Uzi rampage is spawning the triads.