After the first season they will adjust to whatever is normal for your area. This is true for all tubers, bulbs and corms (or perennials, trees and so on)
I was looking at the other thread you started and I assume you are referring to
Anemone coronaria specifically? So I will try to answer both this question and the one in the other thread here. When spring planted the flowering will be much later. This is a Mediterranean plant and when it's on its natural cycle the foliage actually usually appears already in late autumn in my garden. Even though we certainly haven't got Mediterranean winters in Sweden, the plant still is true to its nature, so wants to grow when more moisture is available in the winter and it wants a dry summer rest. For this reason blooms and buds can appear very early in spring once the tubers have settled in. So it's a little bit tender, preferring a mild winter and is not regarded as completely hardy here in Sweden, not even in the south where I live.
USDA zones translates really badly to our climate in Sweden and others could probably advice you much better, but depending on where you look it seems they could be borderline hardy for you, so my suggestion would be to plant them in a sheltered spot with sandy, very well drained soil and you might need to give them some extra protection over winter as well. These aren't the usual bulbs (actually tubers) and their hardiness can probably depend a lot on local factors and how cold and long the winter gets.
