I can't mirror my iPhone on Apple TV?

My dad got an Apple TV (Gen 2) last night and I've done some research about it. You can apparently mirror your Apple devices on it but I can only use it as a speaker (as you can see on the pic, see the icon) with my iPhone 5S and my dad's iPhone 6 Plus. But when I tried it with my sister's iPad Air, the mirror option worked. The icon changed to a TV. It wasn't a speaker anymore. Why doesn't it work for me and my dad's iPhones but it works for my sister's iPad Air?

My Apple TV (Gen 2) is on version 5.3.
My iPhone 5S has iOS 9.2.
My dad's iPhone 6+ has iOS 9.2.

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