I see you are running v10 so there may be some differences as I am running V11.
In any event, not all telephone (carriers) systems are alike. They may use different tone sets, voltages and/or other functional variations that make them unique and subequently may require some settings to be adjusted to make connected equipment (fully)compatible.
In version 11, 3CX has provided a set of templates by which various devices can be configured thereby eliminating some of the pain and guesswork with a wholly manual approach. In the 4114 template they have a listing of countries which can be selected making the device more readily usable. Unfortunately, the Caymans are not one of the listings and I am not familiar with their system to know if it is indeed unique or is the same as one of those listed. Fundamentally, it sounds like the device is not detecting ring and then answering the call. I am guessing a setting refinement is needed.
My suggestion at this point is to call Patton directly and get their take on the situation. While I have not personally had to use their support, others on the forum have reported that they are very good.