I don't think they would although you need to contact your data plan provider to report this. You should report the issue to know if it will be billed to you or not. There are cases where they are people who have been billed as they did not make complains. If you think you have been wrongly billed, you should contact your provider to clarify the issue.
You have to set up an-account with the inmates ID number. You state how much money you are going to put on your credit card to accept calls. You can start with $10.00. The inmate then uses time allotted by facility and you pay for the call. In Maryland, they get 15 mins in the detention Ctr daily.