In the case of most published data, the source chooses one specific primer for development testing of all powders used in a given cartridge. Hornady (#9), Nosler (#8), Sierra (V), Hodgdon, Western, and Lyman (#49), all specified magnum primers in all of their published loads regardless of the powder used. On the flip side, Alliant specifies regular primers in all of their recently published 357 Mag loads.
For many years, Speer has specified a combination of regular and magnum primers in their published data. They specify magnum primers in many of the loads that utilize slower and/or ball type powders, and standard primers for the rest.
One reason reloading component manufacturers tend to specify magnum primers is due to the belief that most reloaders will tend to use "magnum" primers for their "magnum" loads used in their "magnum" handguns.
Another reason magnum primers are specified is related to their performance. In many instances a magnum primer (versus a standard primer) will produce higher operating pressure for a given load. So specifying magnum primers offers a bit of cushion in the case of primer substitutions. If the opposite approach were to be taken (specifying standard primers), higher than intended pressures could result if magnum primers are substituted.
A third reason magnum primers are specified is powder based. Some powders can be harder to ignite and a stronger (magnum) primer can produce more consistent results when those powders are used.
Ed Matunas, who loaded and tested more ammo than most of us ever will, said regular primers give the best results in the 357 Mag when powder charges are 10 grains or less. (The context of this statement was an article stressing accuracy over maximum velocity).