My husband and I left a hose on outide for 48 hours and it burst. When my husband turned the water off, the basement drain must have backed up. Could this be related to all the water draining. Something that looks like soil spit out of the drain with some water. How could we fix this or could this be a one time thing because of the house incident?

It could be just a one-time thing. The drain in your basement may not have been clean and may be clogged if water has not gone down it in a long time. I would suggest purchasing or renting a drain auger from a hardware store and cleaning out the drain yourself before calling a professional.

From your post, it is not clear if any water has gone down the drain. Has it?