It would be helpful to know what you were charged with as that will have an impact on the employers' concern about your record, as well as whether the charge was relevant to the jobs under consideration.
On the whole though, your best option is to contact both employers and explain what they're going to find when they do a background check. Employers being surprised when conducting checks is never a good thing and this way, you have an opportunity to explain and put it in a positive light. (e.g. "I was young and very foolish and learned my lesson. This sort of incident will never happen again."
A person, who is nice to you, but rude to a waiter, is not a nice person. (This is very important. Pay attention. It never fails.)