In BFD and BFDLite, there are a couple of settings that can cause this behavior. In the Play Options panel, look at the following:

"Respond to Groove Notes:" When checked, this option will cause BFD to play back grooves whenever it receives a note in the C5 octave (C5 to B5).

"Respond to song start:" When checked, this options will cause BFD "play along" when you start the transport of your sequencer. Un-checking it will prevent BFD from automatically playing a groove when you hit Play in your sequencer. "Respond to song stop" works in a similar way, but causes BFD to stop playing when you stop the transport in your sequencer.

"Sync to Song:" When checked, this setting sets the host sequencer's song clock as the sync source for BFD's grooves, so that they play in time and phase with the song clock. For example, if you trigger a groove on beat 2 of a given measure, the groove will begin with beat 2 so that it stays in time/sync with the rest of the song (ie, if there is a kick hit on beat one and a snare hit on beat 2, the groove will begin with the snare hit).