Copying my answer to a similar question from the .org forums:
You can’t force WordPress to use iOS emoji for anyone but iOS (or Mac)
users.Emoji are just characters, like any other letter, and how they’re
displayed is determined by the operating system. Each operating system
has its own graphics for the emoji, and they will be displayed using
these.However, to enable emoji in browsers and operating systems that don’t
support them WordPress uses a script to convert emoji to a
backwards-compatible format, and these backwards-compatible emoji are
Twemoji, Twitter’s emoji designs. It uses these because they’re open
source, which is a requirement for WordPress.You can disable these backwards-compatibility emoji with a plugin like
Disable Emojis. When using this plugin emoji will only appear in
compatible browsers (most of them these days), but they will appear in
the original style of the user’s operating system. So iOS users will
see the iOS designs, but Android users will see their device
manufacturer’s designs.It’s not possible to force everyone to use Apple’s designs for emoji,
because these are copyrighted and tightly controlled by Apple.