The entire image in question can be seen here. Under the image is a numbered scene describing the images individuals. The person in question is listed as Moorish Servant.
A little more research into De Sotos expedition leads to this page, which confirms a number of slaves and servants were included in the expedition:
His force also included about 100 slaves, servants, camp followers, and pig herders.
It would seem, combined with the timing you mention concerning the fall of Moorish Andalusia, the painter chose to portray one of those servants as Moorish.
A book from 1853, William H. Powell's historical picture of the discovery of the Mississippi ... By Henri L. Stuart has this passage concerning this:
The Moorish servant or armor bearer of De Soto who is seen behind him in the Moorish costume carrying his master's helmet forms an admirable allusion to the then recent fall of Grenada and the overthrow of the Moorish Empire in Spain It was the fashion of that age as it has been the fashion with conquerors of every age from the times of the Great Empires of Asia for the conqueror to carry in his train in menial service some of the men who were left after the wreck of their national fortunes De Soto did not form an exception probably to the rule then of universal application and it was a happy thought in Powell to introduce him there The very glance at his turban opens a whole field of history to the scholar one glance at the turbaned head would recall to Irving his history of Grenada