Yeah, that's a rhizome. If you originally planted from a rhizome, by the end of the first season you can consider it to have turned into a crown or rootstock as it now has it's own root system and will have formed some buds to produce your new growth for the next season. Certain varieties can produce rhizomes in their second year but usually by the third season your original planting will have accumulated enough excess carbohydrate reserves to make some rhizome growth of it's own. They're one of nature's ways of ensuring survival if the mother plant (the crown) gets wiped out by some force of nature. The second obvious way would be seeds but you need a male to help that scenario take place. If you started with a rooted cutting, you very well may have some rhizomes form during that first year as the fact that it already has some roots to start with, it doesn't have to spend any energy to form a root system and can use any excess energy to put into making rhizomes.
The below pics are of a male I was late to prune this year and thus you see lots of new growth blasting off already from the terminal buds. One tip about your transplant - if you lay them down horizontal like you have, the buds on the bottom of the rhizome will grow out quite a way under the soil before they break the surface. If you were to have planted it vertically, the buds will grow up in a very tight or compact cluster, almost straight up when they break the surface. The reason I say this is that it will help control the unwanted spread as some varieties will send those new shoots a few feet away from the main crown before they surface (when planted horizontally). And over the course of the growing season, there will be new buds that will form along those underground shoots that will continue this spread year after year if not checked. This is the reason folks say they are invasive, which may be considered true - but if you understand how they grow, you can negate this issue with a seasonal underground pruning beginning on about the 3rd year. Hope this helps.