Alexa was too ashamed that they had seen Prince Alex and she kissed. She tried so hard to hide her reddening cheeks, but it's also visible in the naked eyes. Especially knowing that Ramon probably saw it too along with everyone else, she couldn't look anyone with a straight face.
When Alexa tried to hide behind Prince Alex for protection, he knew what she's thinking and feeling. He had to do something for he was the culprit and doesn't feel right seeing her wary of herself.
Prince Alex displayed his prestige and told his bodyguards that no one was permitted to come in; he wanted to have privacy away from the meddlesome eye of everyone.
However, Alexa doesn't feel it's right to misuse his power, other students need to eat too, and its a public place. Even though she doesn't want to face other students at the moment, they cannot stop them from coming and eating.
