Mads,
The plugin does not follow a DAW's tempo map.
Enable sync and the plugin requests a tempo value from the DAW at the beginning of the song. But it is only a single request.
Perhaps you should make a wishlist request
+++ HERE +++. That will allow other users an opportunity to discuss and support the idea.
Note: The link is for the Other Programs forum section so people will not confuse the request for the plugin to follow a DAW's tempo map with the main Band-in-a-Box program tempo map capability.