I don't know when Soundbrenner fixed this, but another user alerted me that the Soundbrenner app now follows a MIDI beat clock sent from BandHelper. This means the SoundBrenner Pulse will change tempo, start and stop in sync with the tempo function in BandHelper. You do not need to use the Send Tempo to Ableton Link setting as before -- just the Send MIDI Beat Clock setting. Then in the Soundbrenner app, go to Settings > MIDI, click BandHelper to connect, and click EXT.
However, for some reason this only works with the old beat clock code in BandHelper, so you have to turn off Help > Utilities > Use New MIDI Beat Clock. I'll post an update if I find out that it works with the new beat clock in the future.