My grandparents were in New York during the 1905 census. What is the earliest movement of West Indies from St. Kitts and Nevis to New York?

Researching the migration of my grandparents from St. Kitts Nevis BWI in the early 1900s to the USA.

Caroline Amelia Hazel nee Nesbitt DOB August 22, 1874 from Nevis and William
Daniel Hazel DOB c 1879 possibly of Saba, Dutch West
Indies. She is found in the 1905 Census as a servant in the household of J
Ingram. She is cited in the 1910 US Census document., She is listed as Black on the
original census form, even though the form attached says White.  She is black.

The Census shows most of the Registrants listed as Patients in the Central Islip
State Hospital. She is also listed as the mother of my late great uncle Daniel
Hazell DOB c 1904 in the death notice of Daniel Hazelle 23 7 1941 in
Manhattan New York Municipal Deaths. The record I have of William Daniel Hazell
indicates that he too was in in New York during the 1905 Census. Interested in when
they left the British West Indies. their USA status, job, how long they stayed
and any other pertinent information. They relocated to Bermuda later
in 1910.  The couple had a son Daneil Hazelle who died in 1941 in New York and
is buried in Silver Mt Cemetery. They also had a son named Clarence Hazelle who
also died in the USA who died in the USA in 1982.