There is no Android app for MB. If the "remote app" you're referring to is the MB Remote plugin (
https://getmusicbee.com/forum/index.php?topic=7221.0) it is just that - a remote CONTROL so you can use your phone to control MB on your PC. Therefore you do not sync anything to the remote app. Questions regarding the MB Remote plugin should be posted on that thread so the plugin developer can address them.
The only way to play tracks on your phone is to sync from the PC to the phone, either using the wired USB sync, or the MB WiFi Sync App (on the Google Play Store) and use your phone's music player. If you want to do two-way syncing, it's only available via the WiFi app. And -only- with PowerAmp or GoneMad players. Both have free trials so you can test before you buy. If you're not interested in two-way syncing, then just about any Android player will work as long.
But again, -playing- music on your phone can be transferred (synced) from MB, but must be played on a music player on the phone.