California missions were staffed by a Franciscan priest or two, and a half a dozen soldiers. The former addressed spiritual and administrative concerns and the latter established physical security for the Spanish interests.
Mission neophytes were often physically punished. I assumed that the military units would have used force at the priests' discretion. However, Lorenzo Asisara recalled that in 1812, Donato, a neophyte at Mission Santa Cruz "was punished by" Padre Andres Quintana with a wire-tipped whip. (Donato then convened a group, planned, and executed the torture and assassination of the padre.)
The source is not entirely explicit about who wielded the whip. Did mission priests administer, not merely call for, corporal punishment?