Revealing mistake: When Kara picks up the Omegahedron, you can briefly see a ring underneath, around her fingers, to make it turn around.
Revealing mistake: When Supergirl falls on the planet ground and gets released from the mirror trap, she gets up and the hard floor stretches down, revealing it's a rubber mat to soften her fall.
Revealing mistake: When Selena uses her magical powers to accelerate the fairground ride to superfast speed, the twinkling fairground lights in the background are also flashing much faster. They obviously played the tape back at high speed to achieve this.
Revealing mistake: When Supergirl is flying to Earth, part of her head disappears due to the blue screen used. Also, some sides of the spaceship either disappear or become transparent.
Answer: It's never explained, she could have changed at super speed. In Superman II, when confronted by the super criminals at the Fortress of Solitude, Superman did a disappearing and reappearing act. So did the criminals. It might be a similar thing.