According to the Straight Dope, they were using the term Indie from the get-go:
Columbus carried with him a passport from Ferdinand and Isabella of Spain, written in Latin and dispatching him “toward the regions of India” (ab partes Indie) on their behalf.
... The original manuscript has not survived, but a printed copy made shortly after its receipt has. In the first paragraph Columbus says “In 33 days I passed from the Canary Islands to the Indies” (en 33 días pasé de las islas de Canaria a las Indias). His first reference to the inhabitants comes in the second paragraph: “To the first [island] which I found I gave the name San Salvador . . . the Indians call it Guanahaní” (A la primera que yo hallé puse nombre San Salvador . . . los Indios la llaman Guanahaní). In all he makes six references to India or the Indies, and four to Indios. Nowhere in the letter does he use a phrase resembling una gente in Dios.
It seems this “una gente en Dios” is sometimes taught in Indian schools, to boost tribal identity and pride. “We’re not called Indians by mistake. We’re called that because our people were so good and godlike.” Something along those lines, I imagine.
Thanks. I recall his description of the land coming first, but I did not know about the passport. Good to know.