It's almost like all the Circles were different and even different Circle mages had different experiences in the same Circle, which is something Vivienne also says.
It's pretty clear the Inquisitor/Trevelyan Human Mage (from playing her) was allowed to see her family and be part of Ostwick society to some degree. Less than if she weren't a Mage, likely, but you have conversation options that reflect it.
We've seen mages (Enchanter or higher - basically those who've passed their Harrowing and never shown any sign of corruption) leave the Circle, with permission from the First Enchanter (which is what Vivienne also says, and Cassandra's dialogue states as well) and Rhys noted they were permitted to go into Val Royeux proper before the whole Kirkwall thing (in Asunder). Clearly, Anders changed things. And, clearly, things in Kirkwall weren't nearly so permissive anyway*, but this fits with what we saw in DA:O anyway. They couldn't just "go wherever they wanted" without permission but they could be and live outside the Circle, and the First Enchanter was the one they needed orders from.
Yes, you can't leave the Circle in Origins immediately, but you just passed your Harrowing, and the First Enchanter has not given you permission. And you're basically nobody.
*The most notable illustration of this is in DA2 if you ask me - there is a Circle mage fleeing the Blight (or something) who tries to go to the Circle for help because she's helping Ferelden street kids. She turns to blood magic and turns abomination (I imagine between the stress of Kirkwall Templars and being a refugee trying to help those kids). But her note basically says she went to the Circle for help willingly, assuming that the Circle would help her, based on her experiences with the Circle elsewhere. Of course Kirkwall just saw a dangerous mage to lock up. But that should not be applied everywhere.