What do Audition/Premiere show as the bit-rate of the audio file in the original source video? What do iMovie/Premiere show as the bit-rate of the audio file when imported back in?
Sounds like possibly the source video is indicating an incorrect bit-rate, i.e. actually recorded at 48kHz, but being identified/treated/exported as 44.1kHz in Audition, which ends up giving it a longer run time. The audio pitch should also be slightly lower when imported back to iMovie/Premiere, possibly not enough to easily notice.
I would check the audio properties in the various tools, and see if that's the issue. If you check the full run time of the clip vs how many seconds extra audio, it would be easy enough to calculate if this is the problem. I would create a project in Premiere where you import the original video (with audio), and import the modified audio as well, and line them up in the same sequence - you should be able to check the properties of the two audio tracks, and spot if the edited track is stretched out overall longer than the original, or if it is some other issue. If you play the project, you should be able to hear if the tracks go slowly out of sync, or if it's some other issue such as jumping out of sync at a specific point.
If this isn't the issue, maybe update the question with info on how the video was recorded, any other tools you might have passed it through, and the exact run times of the original video, original audio and edited audio. I've definitely seen this exact issue caused by 48kHz incorrectly processed as 44.1kHz and vice versa, although it's not an issue I've ever had with any of the Adobe products.