Ah, I see! That's actual fairly normal for remuxing in my experience, although I couldn't tell you why. I don't think it's related to AnyStream though, or OP's issue.
For some reason (i don't know why) mkvmerge adds different delays to the audio depending on the format. For AAC it adds 9 ms when muxing and I have no clue why.
Apparently it's complicated. You can get around the 80 ms delay issue fairly easy, but it needs some tinkering. On a side note you cannot trust mediainfo when it comes to audio delays.
The following screenshot is from gMKVExtract GUI showing the difference when muxing the same MP4 file created by Anystream, with two different programs.
The one on the left was muxed with TMPEGEnc and the one on the rigth was muxed using mkvmerge and as you can see mkvmerge is the one making the delay.
If you look closely on the picture to the right. You will see the video delay to be 80 ms and the audio delay to be -80 ms.
If your only option is to mux using mkvmerge you can get around the issue by doing the following.
1. extract video and audio from the MP4 using FFMPEG
2. mux the extracted video and audio using mkvmerge
If doing so you will get a MKV file looking like this ...
Which is exactly the same as muxing it with TMPEGEnc.
So you would do as follows ... :
To extract video use :
ffmpeg -i g:\your_video_file.mp4 -vcodec copy output-video.h264
To extract audio use :
ffmpeg -i g:\your_video_file.mp4 -vn -acodec copy output-audio.ac3
This will create two files :
output-video.h264 and
output-audio.ac3 which you can then mux using mkvmerge and you will have a MKV file with no delays.