Hello and welcome.
I can't answer your question on the t4000, but is this the device your monitoring company suggested for your panel? Most monitoring companies have a list of one or two devices which they support, they mail them to you, you connect them, and everything is set. Then its up to the monitoring company to get it to work, and no doubt, they have more experience with it than you do.
There are two protocol connections in play here. The alarm panel to the device, and the device to the monitoring company. The alarm panel to the device usually uses contact ID protocol which just takes two wires and is hard to screw-up. Between the device and alarm company may be standardized or maybe not. The monitoring company should be in control of this.
When I signed up with AlarmRelay, they sent me a communicator which they told me in advance only had a 50-50 chance of working with the OmniPro II but it was the cheaper option. It ended up not working, so they sent me a different model that works great, but costs $2 more a month to monitor. They had lots of experience with OmniPro II's and knew what worked and what might work.
Long-story-short, the monitoring company should be in charge of getting this working. If the first one doesn't, they will likely know another one to try.