Close but not quite.
Fastest first puts the top qualifier on the pole, provided he never leaves the track or the pits. If the top qualifier, or anyone else, goes into the tuning area or back to the Lounge, his time is lost and he starts over even though on his screen and others it will still show his fastest lap as the fastest lap for the qualifying session. Going back to the tuning lobby negates all qualifying efforts. This is what most people refer to as a glitch but it's not really. It's not random, it's predictable so it's a flaw in programming. It wasn't always this way, at one time you could leave the track and maintain your position but they changed it with one of the updates for no good reason I can see.
Fastest first also puts you in the order you are on the track if you haven't completed a lap as in the Nurb or other longer tracks. So if 5 people have completed laps and have the slowest recorded times and they stay on the track, they start in front regardless of their times. If faster drivers qualify but leave the track and come back and don't finish a lap, they start from 6th on down regardless of their previous lap time, and will be ordered on the grid in the order they are on the track. Furthest ahead will be 6th etc.
In reverse grid, you always start in front if you didn't compete in the last race. If there were 4 of you new to the current race all 4 would start up front but not sure how the order of those 4 is determined but there will be some logical way, it won't be random. Probably in track position or reverse track position would be my guess.