Thanks for clearing this up Drew. The ATA web site timeline leaves much to be desired.
I have a Trap Shooting Rules book put out by the American Shooting Association, which says organized February 11, 1889, and these rules are revised January 7th, 1890.
During my research of the Money family I found this --
The New York Times for January 24, 1893, reported on the meeting held at Taylors Hotel in Jersey City on the 23rd, where The Manufacturers and Dealers Inter-State Shooting Association was formed. Noel Money was one of the attendees appointed to the Board of Directors, and also the handicapping committee.
This all fits with your timeline.