What does it mean when Qianlong engraved imperial poems and the word Cai on Song Dynasty porcelain?

This porcelain is not the word "Cai" engraved by Qianlong, but the porcelain of Cai Jing, the Prime Minister of the Song Dynasty. In the Song Dynasty, due to Cai Jing's overwhelming power, some official kiln porcelain had the word "Cai" inscribed on it, which actually meant that it was

Qianlong inscribed poems on Cai Jing's special porcelain, but the engraving was not done by Qianlong.