Some of mine are just starting now. They do bloom at their own time. Starting them indoors does tend to speed things up though. Make sure they get lots of sun. The ones that I have just opening, did not get enough sun.

Sure, you can dig them up, and store for next year. If the tubers are firm, they are worthy of saving. I had some that did not do well for a couple of years but this year, they are going gangbusters.