I think we're confusing two things here.
The test is referred to as the "bridge officers test." It certifies that you know the basics necessary to pull a duty shift on the bridge. It is never stated that it confers upon you any particular rank automatically.
I'm afraid the episode makes it more confusing than that. In the opening scene, the whole subject is brought up between Troi & Crusher wherein Troi asks her why "She put herself though all the extra work" in order to become a commander, which she clearly meant as the rank of commander, because she then adds that the rank is unnecessary for being a CMO
Then when she brings it up with Riker, say pairs the both "Taking the bridge officers exam & becoming a commander" Now it's plausible to say she meant commander in the general sense of someone who will commannd, but the previous conversation tends to contraindicate that. She sounds as though she knows taking the exam makes her a commander by rank. Then as soon as she passes, Riker calls her commander, the way one would by addressing them by rank
Now it's obvious that bridge command is a position that can be held at ranks lower than commander, & it's also possible that a sciences or medical officer could hold a higher rank than commander but not be qualified to command a ship, unless they take the additional testing, and such would not demote them to a commander rank.
So it's obvious that the exam cannot be related to promoting to commander, yet in this episode, her case makes it sound like that, that she will obtain the rank of commander by passing this test for serving as a bridge officer
Frankly, she should have never been given command during Disaster
either. Her rank is not relative to command duties, and as such, her qualifying herself for command duties cannot be relative to obtaining this new rank, even though that's what happened. It must be be unrelated, beyond possibly being a compensatory rank bump for the extra training
It's some wishy washy gray area that is never cleared up