Read the ownership clause before you pay the deposit, not when you want to move.
Many molders tie tool ownership to payment in full. Until the balance is paid, the tool is theirs, which is reasonable. The detail that surprises buyers is the mold base. Some shops use standardized or exchangeable mold frames and build only the core and cavity inserts for each customer. In that model you may own the inserts that shape your part, while the frame they sit in stays with the molder.
Neither model is wrong. Exchangeable frames often lower the tooling price and speed up the build. But it changes what you can take with you. If you move, you may need a new frame at the next shop, or you may need to buy the frame. Know which model you are in, and write down what you would receive on release.
Also check what happens to a tool that sits unused. Many terms allow the molder to return, relocate, or scrap a tool after a long period without orders, usually after notice. That is sensible for the shop, and a reason to keep your contact details current and to respond to notices.