There are at least 2 different frequencies FCA uses in the TPMS sensors. Every few years they switch which ones are used in which years.
2016 TPMS will NOT work in a 2012... I have a 2015 1500 and had got a set of 2012 snows on factory aluminum rims for CDN$200, but when I put them on, the TPMS system couldn't read them and the TPMS system "disabled" itself (but nagged me by being the screen that came up on the instrument cluster as the first screen rather than it being the speed). I bought 4 new sensors off a reputable guy on e-bay for CDN$56 and had them installed for $100, work great.
2014 thru 2017 are a different part # compared to 2009 thru 2013.
My 2015 has TPMS sensor Part #: 68249197AA. Which is what your 2016 tires will have. Google the TPMS Sensors for 2012 RAM 1500, and you will find the sensor part #'s you need. Some websites will show you more than 1 part number. Be sure you do NOT get 68249197AA which are for 2014 to 2017.