That's a repeat echo (not reverb) where the feed to it has a bass cut. If there's any reverb at all, it has been added to the entire effect after processing. Mostly it's the first repeat that you can hear, but there is definitely more than one in the loop
You should be able to set this up in Audition without too much difficulty, although it's going to require a bit of experimenting to get it right, I expect. To get the repeat rate right is going to be entirely dependent on the tempo you do the song at - get that wrong and it will sound rather weird...