JP2 provides an open-collector output that is active for 500mS when the start sequence terminates (LEDs go out)
I haven't had a thorough read of the user manual for the timing device you've linked too. However it does appear to have 4 inputs that require connection to an open-collector to operate.
INPUT
1 to 4
Inputs for timing impulses.
Working contacts without potential (short circuit or open collector)
Ex: Manual contactor (HL18), photocells (HL2-31 / HL2-35), Start Gates (H7-1 /
HL7-3), radio receiver (HL610, HL620 etc)
Respect the correct polarity!
Therefore I would say yes my controller board can be interfaced with that timing device. If you're concerned about connecting the two devices togther you can always add an opto-coupler like the one already used on the board to provide an electrically isolated control. However I wouldn't think it necessary.