I believe your assessments are correct. When the Arduino pin is set LOW, the opto LED turns on, and when the Arduino pin is set HIGH, it places 5V on the pin, but the 12V to 5V difference is still enough to turn the opto LED on, thus the transistor remains turned on no matter what.
I will redesign the interface board so that the Arduino side of the interface uses 5V and the relay side of the interface uses 12V as it does now. I expect that will clear up the problem.
Thanks.