Muscbee can't run on a phone, so muscbee specific features like custom start and stop times will not carry over when files are *copied* to a device and played with another player.
One workaround is to convert your files when synching to a device. Musicbee will use the custom start and stop times and trim the files on conversion.
If they are FLAC files, just have MB convert FLAC to FLAC on sync.
I personally wouldn't recommend doing this with lossy files due to quality degradation. YMMV on whether that matters to you.