yes I think they are tubers, you might find that they will not flower for a year or 2 though

Just make sure you don't bury the divisions too deep though, otherwise they will never flower.

You can in the autumn as the leaves die back, - they make stronger roots in autumn and winter. Make sure the new home is well prepared with organic matter though I dont add fertilizer till the next spring. Dig around/under the existing plant very carefully so as not to damage it. Plant in full sun, I find its best done in dry conditions and I remove any debri before replanting, I only select between 3-5 eyes as I find any bigger and they dont seem to do so well. I put the eyes no deeper then 2-3" and water in then I very gently apply a thin mulch for the winter. I would not expect to have flowers for about 3 years.

Thank you very much for your advice.