I found a Georgios Tylianakis age 18 born 1891 on a ship manifest for Ellis Island. He came on the ship Laura Sailed from Patras 25 Feb 1909 He was from Kalmnos He gave a wife Maria as relative in Greece When he arrived he went to a relative: Dimitrias Fio-a-i- cannot make out on the letters 5 Walnut Street Peabody, Mass.
The dates are close enough to your post to be credible. Does his destination agree with your information? I did not find anyone in the Greek white page for Chania/Kalymnos with various spellings of the name. He must have been the eldest son with a first name of his paternal grandfather and the middle name of his father. That is a tradition in Greece.