In 1820 how were the Canons of Durango installed?

I will put out some points and hope that it at least narrows the target sufficiently.

Under the list heading of this document:

Capitulares de la Catedral de Durango mencionados en este volumen. [Google translated meaning:] Capitulars of the Cathedral of Durango mentioned in this volume.

It seems that Agustín Fernández de San Vicente receives this cryptic entry (p.319):

Fernández de S. Vicente, D.José Agustín. Murió Arcediano el 15 de Mayo de 1855 [Google translated meaning:] Fernández de S. Vicente, D. José Agustín. Archdeacon died on May 15, 1855

From this it seems clear that (1) he was canonized as the Capitular of the Durango Cathedral. Furthermore, it must have been before his death in 1855.

Under the same heading, a certain: Dr. D. Francisco Fernández Valentín died on October 21st, 1822 (p.320). Here (p.230), it is this same Valentin:

...who was vicar general of the Vacant See of Durango at the time [...1813...]

Since Fernandez de San Vicente was Vicar Capitular:

...the administrator of a vacant diocese, elected by a cathedral chapter...[o]n the death of a bishop...

(2) It seems he would have officially received that canon only after the death of the current Vicar General. Since Vicar Capitular must be appointed within "eighty days" of the death of the Bishop by the canons of the cathedral chapter to avoid that power passing to the metropolitan, and since we know given what you have written above he was appointed by cathedral chapter, we know he must have been canonized some-time before 80 days after the death of the Vicar General on October 21, 1822. This irregular situation which chose him as Vicar Capitular might explain why there was not oral examination etc.

Next we know that he never took up residency due to an appointment to a secular post as a commissioner in California in March, 1822:

The Plan de Iguala and the news of Mexican independence reached California in March 1822 with a special mail shipment, and the citizenry learned of the formation of an empire (1822-23) under Augustin Comse Damian de Iturbide y Arambara. A Mexican commissioner, Comissioner Augustin Fernandez de San Vicente, arrived later in March 1822…

(3) Since he was sent in 1822 according to this document (p.59), and it makes no sense to have canonized him non-residentially after he had already left on this separate commission, I think he must have been canonized between October 21, 1822 and the end of that year.

This may not give you an exact date, but within this approximately two-month period he must have been canonized as Vicar Capitular of Durango Cathedral. I'm not sure if he was canonized in a previously position which is implied by your claim that he was required to be paid by that chapter in April of 1822.

(4) In response to your question regarding non-residentiary canons, Global Perspectives on Legal History A Max Planck Institute for European Legal History Vol. 5 seems to suggest that those appointed by the crown were considered canons even when they refused to physical go to their see (100-101). Though officially recognized as such, their actual power seemed ineffective against de facto coups.

Here is the Spanish:

Ortega Montañés y la sustitución de la facción de la sede vacante, 1700–1708 El inicio de la gestión arzobispal de Juan de Ortega Montañés, en 1700, fue una coyuntura favorable para el regreso del grupo clerical que encabezaba la curia con su antecesor, desplazando a los nombrados durante la sede vacante. Con esta acción, el arzobispo le dio continuidad a trayectorias de juristas eclesiásticos que servirían de modelo a futuras generaciones. Una consecuencia de tal sustitución fue la serie de fricciones que tuvieron con el provisor destituido, Escalante Mendoza. En 1700, quizá buscando una solución a tal situación, la corona nombró a Escalante como obispo de Durango, la diócesis más pobre y alejada de la capital novohispana. Sin embargo, el aludido se negó a dejar la capital, porque confiaba en una nueva promoción a un mejor obispado. En tanto, el arzobispo Ortega comenzó a desgastar el poder acumulado por el chantre Escalante: no permitió que la congregación de San Pedro, donde el segundo era abad perpetuo, usara estolas en una procesión; después, nombró administrador de la fábrica de catedral al doctor Miguel González, en lugar de Escalante. Igualmente, el arzobispo le dio al doctor Rodrigo García Flores la capellanía del colegio de las Niñas, que tenía Escalante, a quien ni siquiera se le avisó.31 Poco antes de estos sucesos, el arzobispo en persona asistió a la toma de posesión de Torres Vergara de la cátedra de Prima de Leyes de la universidad, misma que Escalante había conseguido para un protegido en 1698 provocando un pleito en el Consejo de Indias.32 Era claro que el arzobispo Ortega había maniobrado rápidamente para formar un nuevo grupo para su curia, el cual estuvo conformado por su provisor-vicario general, el canónigo Antonio Aunsibay Anaya; su juez de testamentos, el cura de catedral José Torres Vergara; el defensor de este mismo tribunal, José Hurtado de Castilla, catedrático sustituto; el canónigo Miguel González de Valdeosera, administrador de la fábrica de catedral; y el canónigo Rodrigo García Flores, flamante capellán de uno de los conventos más importantes de la capital.

And the Google translate version in English:

Ortega Montañés and the replacement of the faction of the vacant seat, 1700–1708 The beginning of the archbishop's administration of Juan de Ortega Montañés, in 1700, was a favorable juncture for the return of the clerical group that headed the curia with its predecessor, displacing those appointed during the vacant seat. With this action, the archbishop continued the careers of ecclesiastical jurists that would serve as a model for future generations. One consequence of such substitution was the series of frictions they had with the dismissed provisional officer, Escalante Mendoza. In 1700, perhaps looking for a solution to such a situation, the crown named Escalante as Bishop of Durango, the poorest diocese and far from the capital of New Spain. However, the aforementioned refused to leave the capital, because he trusted a new promotion to a better bishopric. Meanwhile, Archbishop Ortega began to wear down the power accumulated by the cantor Escalante: he did not allow the congregation of San Pedro, where the second was perpetual abbot, to wear stoles in a procession; later, he appointed doctor Miguel González as administrator of the cathedral factory, instead of Escalante. Likewise, the archbishop gave Dr. Rodrigo García Flores the chaplaincy of the girls' school, which Escalante had, who was not even notified.31 Shortly before these events, the archbishop in person attended the inauguration of Torres Vergara from the university's chair of law school, which Escalante had obtained for a protégé in 1698 by provoking a lawsuit in the Council of the Indies.32 It was clear that Archbishop Ortega had quickly maneuvered to form a new group for his curia, which was conformed by his Provisor-Vicar General, Canon Antonio Aunsibay Anaya; its testament judge, the cathedral priest José Torres Vergara; the defender of this same court, José Hurtado de Castilla, substitute professor; Canon Miguel González de Valdeosera, administrator of the cathedral factory; and Canon Rodrigo García Flores, brand-new chaplain of one of the most important convents in the capital.

However, this occurred some time before Agustín Fernández, and law may have changed. Early in the period of colonization, the possibility of vacant seats seemed common (suggesting a rationale for allowing non-residentiary canons) due to the need to travel across the ocean. Under their entry for 1558 Global Perspectives:

La finalidad propia y específica del cabildo en el derecho vigente es la de celebrar las funciones litúrgicas más solemnes. Tal función, que, como se ha visto, era una de las obligaciones tradicionales del cabildo, se ha preservado procurando que los cabildos llegaran a ser una institución litúrgica modélica.4 Pero lo que daba un mayor prestigio al cabildo era el hecho de que eran los encargados de gobernar la diócesis durante los períodos de sede vacante, que eran con frecuencia largos en Nueva España.5

The specific and proper purpose of the council in current law is to celebrate the most solemn liturgical functions. Such a function, which, as has been seen, was one of the traditional obligations of the council, has been preserved by ensuring that the councils become a model liturgical institution.4 But what gave the council greater prestige was the fact that they were those charged with governing the diocese during vacant periods, which were often long in New Spain. 5

I am not an expert in Canon Law so I may have gotten some of the terms confused, but I hope this helps!