Late response, but if it helps anyone: "istemek" will use accusative case if the direct object is specific (preceded in English by: the /my /your /this /those... and so on). In this example, it is specifically "your making tea" that is wanted, not just tea being made in general. Some Duo examples:
Isn't it rather genitive suffix: Baban needs a noun it owns and that's the yapman.
There is no genitive here. If it was the 'yapmak' in some way the father would own it were 'father's making' with the meaning 'father is making something'.
In this case father isn't doing anything by himself but rather he 'wants' something. So 'baban' is nominative and 'yapmanı' is working as a noun and is accusative.
Strictly literally it would be:
Baban - çay yapmanı - istiyor.
Your father - your making tea - he is wanting.
As usual in the best of my knowledge and hoping it helps a bit. :-)
Where can I see "you" in the Turkish sentence. Is that "ni"? In what topic it was explained, please?