Phil, I have a similar set up, but I have the 17-inch Panasonic SDI monitor. Premier works okay with the T-Tap, with some minor yet annoying bugs.
If I monitor audio via HDMI from the T-Tap, which I prefer, then my Panasonic monitor and its matching audio are about half a second out of sync with the iMac display. (But the HDMI audio is perfectly synced with the Panasonic SDI video.) This is annoying because both the Panasonic and the iMac are directly in front of me, and it's confusing seeing the out of sync iMac image. Definitely not something to show any clients.
If I switch my audio monitoring to "Adobe Desktop Audio," which is the feed from the iMac's headphone jack, this problem disappears. In that case, the Panasonic and the iMac display are almost perfectly matched up. However, now I'm getting lower quality audio, with added digital-to-analog processing in the signal.
Using the T-Tap is smooth and trouble free in Final Cut Pro X, but in Premier it is a bit buggy. That said, it works mostly okay.
While we're on the subject, can anyone suggest the best Preferences settings in Premier to use the AJA T-Tap? I may be missing something.
The CC2014.2 update that we released today includes a fix that should address this issue.