She called on me to tidy my room before I went out. She put the onus on me to tidy my room before I went out. Based on her statement, I knew she wanted me to tidy my room before I went out.

If the sentence must contain "on", then I would use: -She insisted on making me tidy my room before I went out. or -She put pressure on me to tidy my room before I went out.

Put on your jacket before you go out.... Tidy and on do not go together, the two-part verb combination is tidy up, always.