No. That's not how the shell works. Either it will wait for both to exit before showing the (one) prompt, or it will show the prompt after a certain proces exits and finish the other one in the background; in that case you won't get a new prompt after the background one exits.

I'm not exactly sure when it decides to keep stuff in the foreground or run them in the background.

In your case I think it's running both in the foreground, but due to buffering the output from test2 just happens to show up after the prompt