I have tested this in both VPX and MEP, both latest versions, but it may have happened only after the latest updates to both apps. I'm also aware of a number of other users experiencing problems activating the mp4 codec but, in my case, the codec IS activated and "working".
Some background: the project is a Powerpoint Presentation intended for projection as a timed slideshow on a 75 inch UHD TV screen. It consists of graphics, images and videos (apparently a mixture of mp4s and wmvs - I didn't create the PP) but the whole show has repeatedly crashed Powerpoint on a pretty highly specced PC, mine (details in my signature). As a result I have exported the whole presentation from Powerpoint, using the "Save as ..." option, to create an mp4 video file, 1920 x 1080, 29.97fps (so "NTFS", presumably because it was created by an American program).
Testing the exported file I discovered that some of the audio (music tracks) for the presentation exported with audible glitches, so I opened the mp4 in VPX (also tested with MEP) and imported .wav files of the affected music, obviously substituting them for the affected sections of the original audio. Everything played perfectly on the timeline.
I then selected to "Export movie as mp4", using the Default codec and the identical settings to those in the source file, 1920 x 1080, 29.97fps. The only audio codec offered was AAC (not possible to change it), ran the exported file and the audio was running ahead of the video. e.g. there is a person speaking to camera at about 1 minute 30 seconds into the 16 minute, 30 second video. The audio for this speech started almost exactly 20 seconds before the picture! Suffice to say that no amount of "editing" of the VPX project, including moving ALL the audio tracks to start 20 seconds later, allowed the audio to sync to the video. I repeated the export in MEP Premium, with the identical result!
After much trial and error, with no improvement and since I do have the Main Concept mp4 codec installed, though very rarely used, I decided to switch to it. I then restarted the program, re-opened the project (with the audio tracks no longer set to start 20 seconds after the video), chose the same Export (again with all settings as above, including AAC audio) and the resulting file, though showing some deterioration in video quality, played audio and video in perfect sync throughout!
I realise that a Powerpoint Slide Show is a somewhat "unusual" source for a video edit but I wonder whether any other user has met this problem when exporting to mp4, using the Default codec? If so, and you have access to the MC codec, does it solve the problem for you? If this is a problem affecting other users as well, I will raise a support ticket with Magix since, on my system at least, there seems to be a major problem with mp4 export and the Default codec.
Jeff