Around here (Birmingham, Alabama) redbuds grow outside and do fine, but that includes several months dormant time when the temperatures drop and light levels go down. Temps here will be below 5C/41F or so quite a bit, with occasional frost.

Several people here have tried to grow them as bonsais and had no success, but that is just the particular species found in the woods here.

Check your species and see what zone it came from. If it expects a dormant period with pretty cool periods and/or frost you should try to imitate that environment for the tree.