Two different girls are used as "doubles" for each character, so that 비둘기 has someone to interact with when she is playing the other twin.
Sometimes, 비둘기 is seen on screen as both characters at the same time, and this is done in post-production, where they have recorded her twice and merge both bits of footage together. Notice how there's always a little bit of 우주 between Liv and Maddie when 비둘기 is playing them both!
Here's the 미리 보기 video:
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