How does function calling actually work for the Assistants API?

Fine-tune models cannot be used in the Assistants endpoint.

Developer fine-tunes are more likely to damage the function training than to improve it, without devoting experienced labor to the development of training example sets (one discovers when they are used on the chat completions endpoint).

For improving the quality of tool-calling, you have the function specification itself, the name and the parameter names within, and the description text of parameters, to make the utility of the function and the expected return value extremely clear to the AI.