She did not tell the details to the second Prince. She simply said that Prince Lan Wencheng wanted to make her his first concubine without mentioning that the Prince was only interested in her because of what Lan Zihao did with the dragon rain last night.
Seeing how Lan Zihao looked surprised after hearing the information was enough for her, and she didn't need to start a fire between the two Princes by saying that Lan Wencheng might not be serious about his plans and might just want to provoke Lan Zihao.
'Prince Lan Zihao created the dragon rain when I danced last night, and perhaps Prince Lan Wencheng is just curious about the reason behind the sudden rain that his younger brother created. If the two of them end up in conflict, I shouldn't put myself in the middle,' she thought as she walked back to the pavilion where the girls from Tiantang House stayed.