As a tenant that resided at an address for more than 1 year, Am I responsible to pay for the tile in the house to be cleaned from my deposit?

Depends on how dirty you left it. If you tracked mud, dog poo and other nasty stuff over it for a year, then left it that way without cleaning it when you moved, then yes.

Most leases specify that a property must be left "broom and mop clean" so if your landlord had to come and chip dirt away, or get on his hands and knees to scrub away gunk, yes, you can be charged for excessive cleaning.