I can say that Browning started having shotguns made in 16 gauge in the year 1909.Winchester started having the model 12 shotguns made in 16 gauge in the year 1914.so I would surmise that the time frame of 1909-1915 would be the correct time frame for the introduction of the 16 gauge shotguns.
You need to find more information about the firearm. Winchester made 25 different models of the "94" and they were not shotguns. Models like the 9410 were. Contact winchesterguns.com for some answers. * Ignore the first answer. A 16 gauge Model 94 is a Stevens/Savage shotgun.
The gauge of a shotgun is directly related to the size of the barrell. In the cases of shotguns the sizes going from biggest to smallest for 'standard' (not all) shotguns is. 10 gauge, 12 gauge, 16, gauge, 20 gauge, and a .410 bore shotgun (410 is not a gauge but a caliber)