How does changing the altimeter setting in the US and elsewhere compare?
Indeed the US and the rest of the world handle this differently.

In the US, if you are cleared to a flight level or altitude, you change the altimeter setting as you are about to cross the transition level (18,000 @ 29.92).


  [When] descending, even if cleared to an altitude at the time the cruising level is vacated, the altimeters will remain on standard pressure until just prior to the transition level.


Unless cleared in a climb to FL180, then the change is done a bit earlier.

In Europe and elsewhere, the change of the altimeter setting is done as soon as you start climbing or descending to the cleared flight level or altitude.


  
  climbing and cleared to a FL - set Standard Pressure Setting (QNE/1013 mb);
  descending and cleared to an altitude - set QNH.
  


Between the TA and TL no altitude/level can be assigned. If the local pressure is too low, what floats (rises) is the TL.

The same for the US:


  If the altimeter setting is lower, the lowest useable FL becomes FL190 or even FL200.  This restriction ensures that a minimum of 1000' vertical separation is maintained between the aircraft at 17000' on QNH and the one at the lowest useable level on Standard Pressure Setting (QNE).


If the TL is FL150 as in your example, you will not be cleared to 15,000 feet. You will be cleared to FL150. Based on the above, you will maintain 1013 (QNE) until cleared to an altitude. The same for the US, you won't be given an altitude of 18,000, it will be FL180 whether going up or down.

(Image source)



Source: SKYbrary.aero