It is not exactly clear but I believe what you are doing is making a recording using Presenter Video Express and while recording either you are playing the video on your system directly using some player or you are playing the Presenter's published output containing that video.
Now while the video is getting recorded, audio which gets recorded along with it, is actually the audio playing from your computer system and not the one embedded within the file.
Also it is better if you directly import an mp4 video. It should not result in any deterioration in the quality. See this link for more info- http://helpx.adobe.com/en/presenter-video-express/help/recording-videos.html#insert_video
However, if you already did an import of video in Presenter Video Express rather than recording it, under your Preference setting of Presenter Video Express, you have the option to enhance your video quality and reduce audio noise.
See this link for more info- http://helpx.adobe.com/en/presenter-video-express/help/setting-preferences.html
Please mark this answer as correct if you find it useful. Let me know if you have any further concerns.
Adobe Presenter Engineering Team