Clock out is not a MIDI clock out. It works on a voltage, whereas MIDI is digital. Luck dinsync and MIDI use different pins and MIDI cable usually only have the 2, 5 and sheild connected, as I really can't imagine it's too good for a synth to cross-plug the two. I moved some stuff around and replugged my MIDI cable into the clock out. I use cheap din cables from an electronics store as MIDI cables. They have all the pins wired. Shit went weird and I really freaked out for a sec. I turned everything off and on again which made things fine again, but it really left stains in my underwear.
If you want to sync your circuit to the BSP, you may need to split the MIDI signal somehow, like with a splitter box, then see if the Circuit has a way to make it ignore note data on it's in. The other way is to set all your BSP sequencer's channels to one different to those you have assigned the Circuit tracks to. If the Circuit has a THRU function, you can get away with not using a splitter and sending on the BSP data via the Circuit.