"He would sprinkle his private parts with it." Shaikh Ibn As-Sunni said: "Al-Hakam (one of the narrators) is Ibn Sufyan Ath-Thaqafi.

The purpose is to ward off devilish whispers lest the person think any emission has taken place, and thus think that his Wudu' has been invalidated.
Sunan an-Nasa'i Book 1, Hadith 135