Burkholder's Spaniards in the Colonial Empire says: "...competitive examinations (oposiciones) began in Mexico in 1575. Prior to participating, competitors had to document their limpieza de sangre. During the exam they had to demonstrate knowledge of moral theology and administration of the sacraments plus their skill in either Nahuatl or Otomí."
The concourses were announced by circular letter. The qualifications of a learned "opponent", or examiner were printed: "Certificado impreso de los meritos del bachiller don Francisco de la Peña, cura del pueblo de San Pedro Tlasquapan, opositor del concurso de curatos vacantes en el arzobispado de México."
Brading's Una Iglesia asediada describes Michoacan diocesan hiring as follows: Some of the high clergy from the cathedral chapter were synodal judges in charge of hiring. The bishop picked from the three candidates they referred to him, then sought the viceroy's approval.
Still, I doubt the above was unique to Mexico, and for all I know the concourses are still going on.