To freelancers, is it necessary to ask client to initiate the contract before doing anything else?

Hi guys! I need your opinion on this. I got my first project that I have to collate 200 info of clients online, which, I delivered on time. I got paid $10 (Awaiting milestone status) ~ I don't know what this means. Sorry, I'm new to this.😁 Later on, I was also asked to send emails to these clients, which was not part of the agreement in the first place. However, I am not complaining since it was an easy task.

I asked the client how we'll go about doing the succeeding task after the contract. He told me to continue what I'm doing and he will pay me accordingly.

Question: Is it rude to ask the client to initiate the contract before I do anything else? Or is it just practical to do so?