We are talking about generalities and the OP chose the year 1958 in the title. It just happens that 1958 is the year the first modern Japanese SLR's were introduced, Nikon were a few years behind their competitors with the release of their first SLR in 1959 and you're probably over estimating their importance, not all professionals used Nikons quite a number used other makes including Pentax, and others never used 35mm at all.
1958 was the year that Japanese camera manufacturers began to export en-mass to Europe and North America with models that appealed to the market. It's not one company in particular but a deluge of models from a growing number of Japanese manufacturers from 1958 onwards.
If we wanted to be more accurate it would probably be better to say that the period between 1958-61 is the time when the modern SLR matured, particularly with the first Japanese camera to have TTL metering the Pentax Spotmatic.
Nikon's F was a 35mm system camera with lenses and accessories suited to almost any imaginable professional use--that's what sold them. Pentax and Minolta didn't come close in the late 50s/early-mid 60s.