I cannot duplicate this behavior. All mouse clicks and keyboard presses are ignored by CQ100 if the program does not have the focus. If people were seeing intermittent transmissions from you while you were using some other program, the only explanation is that CQ100 was in VOX mode and not QRT.
Remember the mode is stored by band, so if you went to QRT mode on one band, then switched to another band, you may not still be in QRT mode.
I suspect your mic was hearing your speakers and trying to trigger VOX transmit on this sound. CQ100 refuses to allow your transmit when the frequency is busy, so the other station continued talking. When the other station said OVER, your vox delay keyed you on-air for a second, but everything was now quiet so your vox went off-air after this quick key-on. It sounded to everyone that you were asking for a break to get into the conversation.
Perhaps CQ100 should be designed so it will never transmit unless it has the Windows focus. Or perhaps the VOX mode should be removed entirely.