I typically invoice a client for 30 days after completing each phase of the product design. If I do not know a client, I may ask for a percentage upfront.
As I have not seen your concept, I cannot comment on the cost of the CAD work. If it is very simple, the cost you were quoted maybe too high. However, A complex assembly that requires lots of surface modeling (aesthetics) will cost more than a simple functional concept. If this product requires motion analysis, FEA, rendering (for marketing), etc., expect to pay for those extra services. Solving the problem at the design phase is much less expensive than at the production phase.
If you are selling thousands of these product, it is less expensive overall to hire a good designer than to pay more later in development (rework, tooling costs, returns, etc.). A large design firm may charge considerably more than $13k. It costs us thousands of dollars a year for software and equipment maintenance.
What CAD software does this firm use? I use both SolidWorks and/or Pro/Engineer for 3-D CAD models, and this software is widely used at well known design firms. If you have a specific question, you can send me a message.