This is a total non event.
If he was CLEARED for take off after 1.20, then give or take a few seconds, he would have become airborne exactly 2minutes behind the heavy. Which is correct.
What some pilots fail to understand is that vortex is timed from rotation of the 1st departure to the rotation of the 2nd. So the take off roll is included in this calculation. Of course you may want extra time in certain situations which is never a problem, as long as you tell us before you line up.
I speak only for the UK, but this is how controllers here are trained.