When you said "I also assume a 9 speed cassette isn't going to work too well, but is it really going to cause problems?" did you mean '10 speed cassette'?

Did you pay for a 9-speed cassette? If so, they should have sold you one. You are right to go back. If there is a delay in getting the cassette you want, if they are a really good bike shop, they'll loan you a cassette you can get by with until it comes in. In any case, don't be satisfied with this and give them a chance to fix their mistake.