Make sure I have it right. You are running the MIDI out from BIAB INTO your synthesizer? Why? Your interface has MIDI in and OUT on it. With your BIAB's MIDI data being sent through your synth you are getting collisions between note on and note off message and that is what is causing the hanging notes. If you want to have BIAB play other sounds from your Alesis, patch from your interface MIDI OUT to your Alesis MIDI IN and make sure the channels match up.

My thought on hanging notes is that perhaps your BIAB has generated a note on message for note 65 (to use a number) and you then manually play a note 65 (which is F above middle C) and release that key. You had the original MIDI note on message, then you manually played that key again, which sent another NOTE ON message, and let go of the key, which sent a NOTE OFF message, but that original NOTE ON is still on and the note is still playing and will keep playing until it gets another note off.

You can actually cause that manually to test what I mean. Press a key on your keyboard and while depressing that key change MIDI channel on the Alesis. When you let go of the key the original note SHOULD still be playing because the original depression of that key on MIDI channel X never got the corresponding off message because you changed channels and can no longer send the note off.

Start by remembering that MIDI is not sound. It is on and off messages. And synthesizers are not really "musical instruments" per se, like a piano or a guitar that create sounds with strings that vibrate. Synthesizers are essentially computers that are configured to synthesize and play sounds. Right there in the name. They synthesize sounds. With a data stream.