Your understanding should be correct, but there are some limitations, namely that:
- It has to be your first heroic dungeon of the day;
- You have to random queue for it;
- It has to be a level-appropriate dungeon (i.e. WoD dungeon at lvl
From the patch notes:
You can now earn bonus reputation for your first dungeon and scenario
of the day. You can select which reputation you choose to champion by
selecting it from the reputation panel on the character screen. When
you queue for a dungeon or scenario, the UI will remind you which
reputation you are championing and allow you to change the reputation
from there. (You cannot change that reputation once you are in the
dungeon or scenario.)
Also see this thread for more information, including the indication that the process still worked post-MoP, and is my source for the third requirement above.
I cannot find any indication that this feature was removed (for level 91+) or altered in the last six months, so I have no answers if you're meeting those three requirements and still not gaining reputation.