I think Bottlecaps had a good suggestion, that you can ask the parents about disciplining their child when you make the babysitting arrangements--one of those standard questions along with dietary restrictions, naptimes, medical conditions, etc.. It doesn't mean you expect their child to misbehave, just that you want to be prepared for it.
And the other part of it is what rules you, as the babysitter, have, and what ways you've already thought of to discipline kids. For example, like you said when you were at your sister's house, you didn't really have a "room" you could send the kid to for a timeout. So maybe you have to think about a different place to put a child for a timeout, like a chair facing the corner in the kitchen, or a couch at the unused end of the living room. Since kids might be coming in from a variety of families with different rules, I think a warning on the first offense would be appropriate--"Simon, that is back-talk, and I don't allow back-talk. If you do that again to me, we will go straight home instead of getting ice cream." And then if he does it again--follow through on the consequence.
Most generally well-behaved kids will pick up on new rules quickly if you explain them, even if they're different from at home. The original kid sounds like a bit of an extreme.