it is likely that the pre-flash on your SB-600 (used forr the TTl flash metering control) is triggering the lights just before the camera actually takes the picture.
You might be able to turn the pre=flash off by pointing the flash head on the SB-600 up wards or to the side.
It may also be the case that your new lights slave eye is not functioning, that the units are not working (can you test fire them?).
I did test them and they fire.. I hear them beep when I shoot. I tried turning the flash behind me, straight up. I was using my Husband as the subject and he said the same thing, the lights fired before the camera snapped.. Is there a setting I need to change?
Pre flash is triggering the other flash before the shutter opens. Put your SB600 flash in manual mode at low power and disable any red eye prevention. There is no TTL metering in manual mode and thus no pre-flash. Or, alternately forget the SB600 and trigger one of the monolights via cord from the PC connector on the camera or buy a radio trigger.