Was there an option for the safety to be moved automatically to the safe position when the action was opened on the pre 1913 models or were only manually positioned safeties available?

The "Combined Automatic and Independent (3 position) Safety" was patented by Alexander T. Brown and Wilbert Smith in 1886. It was an option from 1886 to 1895, then was standard from 1895 to 1902. Thereafter, it was available as a special-order option until 1945, and is frequently found on pre-1913 guns.
The safety automatically returned to the middle (safe) position on opening the gun, unless the slide was in the rear position.

The two-position safety used after 1902 returned the safety slide to the rear (safe) position.

The safety on HOT guns was NOT automatic.

"The safety on HOT guns was NOT automatic."

But could be ordered from Hunter Arms.
When I was editor I wrote about how the safety on a HOT did not return to safe after firing and opening gun, a gentleman contactred me and send me picture of a Specialty Grade that he had that had an automatic return .

Never say never.