>You don't typically put a tajine in an oven. You place it over a fire or on the stove top.<
Depends on how "authentic" you want to be, FF.
Technically, tagines are used over charcoal braziers. There's a name for them in Morocco, that I alway forget. But, basically, they're confined "stoves," with a top opening that the tagine base fits into. This kind of set-up allows a minimal use of fuel, and slow cooking.
In American homes there is rarely an equivalent (although some folks use their charcoal grills).
Cooking on the stovetop is the preferred way. And, as you say, you start with a cold tagine, and let it come slowly up to heat over a low flame. But with fully glazed tagines that's a problematical approach unless you have a good defuser. That's when the oven comes into its own. Again, the best approach is to start with a cold tagine. Put it in the oven, turn the heat to 250F, and go away for a couple of hours.
The drawback to using the oven is that the tagine doesn't operate in its most efficient way, because the conical hat is heating as well as the base. The whole idea is for the top to be cooler than the base, so that the evaporating liquid condenses on it and runs back down into the food.
So, given a choice, it's always better to go with an unglazed tagine and use it on the stovetop.
Probably the major difference between tagines and braises we are used to is the matter of browning. Tagine ingredients are rarely browned. And when they are, they are done so after the cooking is complete, rather than beforehand as is usual with braising as we think of it.