Yes it might be a minor bug… hard to say But I'm inclined to think it's not.
If for example you open a painting where the Pastel tool was the last tool used, it will have that tool already selected. If you now switch to a different tool, say the Oil Brush, and then close the painting without doing anything else, even if you hit Save, when you reopen it again, the Pastel tool will once more be selected.
Likewise similar things happen with other tools like the Perspective grid.
In this respect AR is treating the Symmetry tool in the same way it would these other tools.
So this may be intended behaviour.