In reply to:

what are the dates of the decade known as the "nineties"? 1990 to 1999, or 1991 to 2000? now, what
do you think the years of the 20th century are (were) 1900 to 1999, or 1901 to 2000?


By this reasoning this should be the 20th century we just entered and 1999 was the last year of the 19th. ¿Qué no?