@Sardis please use this thread to ask questions about game mechanics. I am always ready to explain my as DM choice.
You can read for example
this article or dig more, but I'll try to explain in my own words below
Charisma (Performance) is to impress audience. You don't need to impress a beast. You need to play single tune in order to trigger the magic. That is no way a charisma (performance) ability check.
As an example see
Pipes of the Sewers magic item. It say "You must be proficient with wind instruments to use these pipes.". Assume flute Archfey posses is a similar to that magic item, but simpler to use, so you can attempt to use it even if not proficient.
Now as a DM I had to chose one out of 6 abilities: Str, Dex, Con, Int, Wis, Cha for the ability check. Your DM picked Dex as most appropriate.
Does that make sense?
P.S.
I would probably consider allowing to add sleight of hand prof. bonus, but as far as I see none has it. Does anyone?
