Can it happen that we don't own the IP rights to our code?

Depends on what IP rights you sought, copyright is a pretty standard "work-for-hire" arrangement but what about the preliminary UX/UI skeleton drawings (potential tradedress), or the beta-customers (commercial trade-secret). Ownership can be nebulous in that some software requires underlying libraries which may have licensing / distribution constraints. In Europe moral rights also come into play but that is rarely invoked. In short, the 3 you need to focus on are copyright, trade secrets and trademarks/tradedress (UX/UI) to make sure the assignments are evidenced in writing (contract) and formal registrations are under your company name.