Enjoy your first flower. Then, chop the vine back to the first leaf node. Apply a fertilizer (a rose or tomato fertilizer work fine). A couple of weeks later two new shoots will grow from the node. Pinch them back to their first nodes. Do this at least 2 or 3 times during the growing season.

This fall plant your Clematis deeper, so the crown is 2-4" below the surface level. Next spring cut each shoot back and pinch all new growth.
This treatment is recommended for all new Clematis until they get established (2-3 years). After this, you have to prune it depending on the type - we will need to know the name of your Clematis to give you an advice.
Good luck!

Are you able to post a photo? I can't tell exactly from your description what's up but if those "finger-like twigs" are indeed roots, then the vine has not been planted correctly and you really do need to make some corrections. The deep planting demanded by clematis is what typically ensures the development of multiple shoots from the root crown as well as a better, healthier root system and increased disease resistance. You should never, ever be able to see roots at the soil surface.

I agree, if roots are exposed you'll need to repot it now rather than in the fall.

Clematis tend to produce few scraggly vines unless pruned hard at least for the first few years.