Dynamic Linking audio from Premiere to After Effects can be tricky, especially when there's more than one audio track. In After Effects, if you open your Effects Panel, are there any effects applied to those bottom (audio) clips? Are they arriving into After Effects as just empty audio? I wonder what would happen if you unlink them in Premiere and then right click > Replace with After Effects Composition each individual audio track at a time and see what happens. I'll try it out later with one of my video files if you don't have any luck with that.
Oops, I forgot to mention that I think you need to have a video track selected for dynamic link. But looks like you already knew that from your video.
Hmm...well I'm baffled why it's doing that. Another idea: Highlight the audio clip in Premiere, and copy it. Then in your After Effects composition hit paste. Even though you're in different applications, the audio should paste into your After Effects comp.
I've had similar problems before. If I remember right, the only workaround I could come up with was to bring the After Effects comp back into Premiere, and then sync the video with the audio. Or in this this case, since you are doing the "Replace with After Effects Composition" option, to leave the composition in your Premiere timeline, and keep the audio edit there. So in other words, you would do the visual work in After Effects, and the audio work in Premiere. Editing audio in After Effects is kind of a pain anyway.