Visible crew/equipment: When Selena visits the school, there's a tube reflected on her window. When her car starts to move we see it's part of an umbrella-like structure used for lighting.
Visible crew/equipment: When Supergirl first starts "flying", her movements easily reveal the use of wires to give the effect.
Visible crew/equipment: During the tractor scene, a wiggling boom mike is reflected on the bar's mirror.
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.