Sure, antidepressants can trigger and/or exacerbate mood swings. The problem he is experiencing could be due to bipolar or his cymbalta, OR it could be a combo of both.

Whatever the cause is, I'm sure his symptoms will clear. BP might be a lifelong condition, but it does not mean you experience symptoms 100% of the time. They may come back again, but they won't always be there. I think he'll be ok, especially since you're very caring of him.