I had her make chicken for dinner. (Does it mean the chicken is ready? Could it be used in a different context?)

Hello, dear members of this forum!
I'm trying to learn whether the phrase "have somebody do something" in the past "had" means that the action has been completed or whether it could also be used when the action has recently begun.

A context:

Person A is coming home from work.
Person B is waiting for A.
After A comes (has come?) home, B says "I had [person C] make chicken for dinner".
The chicken is still being made (it hasn't been made yet). = Person C is still making chicken. He may have started five minutes ago or so.

So is it possible for B to say "had" even though C hasn't made the chicken yet (he's still making it)?

Thank you very much!

It is possible.

In this context "had" somebody do something means you asked or directed them to do it. For example:

1. Since the hotel offered a shoe cleaning service, I had them polish my boots.

2. I had the dentist extract my painful tooth.