Good news on the Blue common wire stuff. Here many years ago I had some power stealing issues with the RC80 and installed the HAI power supply board / Elk 24 VAC transformer so the wiring here is a bit different but similar.
Here I have multiple inside and outside HAI temperature and humidity sensors. They are set up in the zones section as temperature or humidity. (they are below and above zone #16 - IE: zone 13,14,15,17(1), 18(2)...and so forth). IE: these are set up only in Zones section and no other section.
The Thermostat is set up (under ZONE) as default (left alone - do not name it in ZONE section) and AUX in the ZONE type. It has to be configured this way per the HAI Omnistat documentation.
In help section of PCA:
When any Thermostat Type is changed from the default setting of Not Used, Zone 16 and Output 8 are automatically configured for thermostats on all HAI Controller models except the Omni LT. There is no need to change the Zone Type for Zone 16 or Output Type for Output 8.
When you change the zone #16 device name/description or from AUX to something else the panel assumes its some other device and doesn't know its a thermostat.
Looks like you are almost there. Here is what you should see. Note Snaplink example is multiple thermostats.
The answer here is the same as in the thread above which is IPhone Snaplink specific.
BTW I mostly just look at the settings and leave them alone these days. Due to WAF temps are set at 68F during the summer and 70F during the winter here in the midwest. No setbacks are used anymore (WAF thing). 68F isn't even cold enough as wife gets up at 3 AM sometimes in the summer and turns on the ceiling fan in the master bedroom causing a wind chill effect.
My Thermostat name comes from the Thermostats section. I called it thermostat. Call it something else if you want such that you see the name in your Omnitouch 5.7e. (well like Tstat or thermo or anything else).
Please note that the changes are not dynamic; you have to save them and then upload them to the panel to see them working.
Now that the TSAT is connected I changed it to "Energy Saver" and even discounted the dinning room window that was attached to Zone 16 just to be sure that was not the issue.
I also renamed that Zone to 16/TSAT it was 16/TEMP I thought that maybe calling it a temp caused the OmniPro II to interpret it incorrectly.
Side comment here unrelated / related. I have switched much of my stuff over to Ubuntu 14.04 64bit. Goofing around installed PCA and Snaplink in Linux Wine and they work fine (well even faster than Wintel) in Linux. So you can configure in PCA in Linux and even use Snaplink in Linux.