Comcast Digital Voice/ADT alam system

I switched to Comcast Digital Voice, and I have an ADT alarm system. I rewired the alarm from the outside box and spliced it into a standard telephone cord, the cord plugs into the back of my Arris modem.
I tested the alarm by calling ADT (on my cell phone), warning them I was going to test it, and did so. They got the signal, no problem. I had plugged my single house phone into the second jack in the Arris modem, got a dial tone. Bam! I'm done, right? Now here is where it gets funky.

Over the next couple of days, my friends were telling me that they were leaving messages for me at the house to no avail. I figured out that the house phone wasn't receiving calls. I could call out, but I couldn't receive them. There would be a single blink on the Tel2 light when I called the house on my cell phone, but the phone never rang.

When I swapped the ADT line and the house line, I could make and receive calls, but the ADT line (in Tel2) couldn't call the alarm center.

So:

Tel1 seems to work fine.
Tel2 can make calls but not receive them when the house phone is plugged into it, but can't make calls when the ADT line is plugged in.

I tried using a simple phone jack splitter in Tel1 and it seems to function identically - it has the same problem. This makes me think that the issue isn't simply a modem issue.

Ideas? Should I reverse some of the wires for the ADT line?