Templar Order is a military order, where subordinates obey their superiors. Circle mages have leaders, but you don't swear any oaths to obey orders and a mage isn't breaking any oaths by abandoning the Enchanters.
There were Templars that did stay in their Circles in order to protect the mages and tranquil. We see this in an Operation where the Templars, unaffiliated with the rogue Templars or rebel mages, stayed in their Circle to protect the mages who wanted to stay. Even when mobs formed outside the Circle, the Templars kept vigil.
There were many Templars that stayed loyal, just as there were many mages who stayed with the Circle. However, unlike the rebel mages, rogue Templars did swear themselves to the Order and couldn't just up and leave like many rebel mages left Fiona. Well, some did, but they were either crazy, thought of something greater than their oaths, or just didn't care about vows.