To clarify, the kiosks don't replace the immigration officer they just make it so meeting with the officer can be super quick. The computer in the kiosk checks your identity and verifies other info.
After using the kiosk you still approach an officer who may ask a few questions. The officer, however, doesn't need to scan your passport or punch away at a computer like they usually do - human labor is reduced and lines are made shorter. More info here:
http://www.cbp.gov/travel/us-citizen...rt-control-apc
If your flight is on time you should have no issues. The kiosks have cut wait times across the board, not just for people using them, because the immigration hall is still staffed the same as before but the officers now have less work to do. I really wouldn't overthink this! If you're running late just have your husband use his British accent to charm the JFK employees.
Here's a link to an article on the success of the kiosks:
http://www.amny.com/transit/delays-a...osks-1.7295860