Sorry Castle, there were almshouses before that date. Richard Watts (1529–1579) left money in his will (dated 22 August 1579) to improve the existing almshouse in Rochester, so a earlier date than 1594 is almost certain. His will refers to "the almshouse already erected and standing", desiring it to be "reedified" [rebuilt] as well as extended with rooms for the travellers.
Depending upon your definition of almshouse, Richard Pontyn left money in 1315 for "a House with Appurtenances called the Spittell of St. Katherine of Rochester in the suburbe in Eastgate" for any "Man or Woman of the Cittee of Rouchester to be visited with Lepre or other such Diseasses that longe to Impotence". Now this may be best known as a leper hospital, but "other such Diseasses that longe to Impotence" indicates a more general refuge for the sick (including due to old age). Pontyn's bequest became St. Catherine's Hospital (actually almshouses) which was amalgamated with the Richard Watts Charities on 1 August 1975. The Hospital is still functioning under RWC's aegis in the almshouses at the top of Star Hill, Rochester.