Where did "Chinchew" come from?
泉州，簡稱泉或鯉，又稱刺桐城、清源、溫陵。
Although 清 can be transliterated as chin, it does not seem to be the reason.

Quanzhou, formerly known as Chinchew.
The Postal Map name of the city was (note: should be "is") "Chinchew", a variant of Chincheo, the Portuguese and Spanish transcription of Chiāng-chiu.
It is uncertain when or why British sailors first applied the name to Quanzhou. Variants include Kangiu, Chinchu, and Chincheu.

所以，Chinchew 是從葡萄牙語、西班牙語的 Chiāng-chiu 轉譯而來。