It wasn't that way at my father's installation, an army arsenal and research center.
[BTW, a "standard" Touch-Tone phones does not have the fourth column. Further, plenty of Touch Tone phones introduced in the early years had only 10 buttons, not 12. We had such a set at home.]Anyway, my father's installation was all rotary dial served by a cord switchboard dial (SxS) PBX accomodating several thousand extensions.
The Autovon lines came in on trunks that were no different than the city trunks and were handled the same way. There were no special signals for priority calls or ways for priority handling. As mentioned, telephones were plain rotary.
To reach Autovon they dialed 8 then the Autovon number. For their purposes, Autovon was merely a switching tie network to other govt installations.
All incoming calls went through the PBX where the operators connected it to the desired extension. Because of the high volume of extensions, an extension itself didn't have an appearance, rather a dial trunk did. That is, if you wanted extension 7182, the operator plugged in the 7 row and dialed 182. I've seen other cord switchboards serving very large PBX set up in a similar fashion.