Hi 👋🏻 your sentence used this phrase correctly. Good job! Ultimate say is the ‘final say’, or the ‘last word’. What they say holds the authority to make the final decision.

It's like when I was a kid, if I wanted to do something with my friends, my dad had the "ultimate say" if I could go or not. So I guess the meaning of "ultimate say" is that if someone outranks your authority, you can want to do something or permit something; however the person with more authority (higher position than you ) really has the "ultimate say"