Duggap, a possible explanation is that in 1875 or 1876 the Steele-&-Johnson Mfg. Co. produced those buttons in fulfilment of an Army purchasing-contract which was signed just a month or two prior to the issuance of the Army 1875 Regulations design-change for Enlisted-men's uniform buttons. I do not know the exact date of the Regulations-change... but for the sake of discussion let's say S&J gets a button order from the Army in October 1875, and in November the Regulations get changed. S&J fuflils the October contract for buttons with the design specified in the that contract, using the company's 1875-and-later name in the backmark on those buttons.
That is just a theory, but it's the only explanation I can think of.