The Armenia situation is a perpetual headache when studying the Sasanian period. Nominally, Philip the Arab had ceded Armenia to Shapur following the former's defeat in 244 AD, however, what the Romans had in mind was a semi-independent Armenia, with a king picked by the Sasanian King of Kings, and crowned by the Romans. This arrangement seems to have been agreeable to neither the Sasanians (Shapur's inscription mentions the "lie" of Philip) nor the Arsacids.

At least nominally, Tirdad II was supposed to be succeeded by his issue Khosrov, but the latter was murdered by Shapur in 252. Touraj Daryaee mentions in Sasanian Persia that Shapur "installed a ruler called Tirdad" who reigned from 252-262. But Encyclopedia Iranica says:

During the first phase of the war, Šāpur must have retaken Armenia and appointed his son Hormozd-Ardašir as the “Great King of Armenians,” a prestigious title created evidently to placate the proud Armenians.

There's some, uh, elaboration on the various theories:

The ŠKZ refers to Hormozd as the “great king of Armenians,” a position that he must have acquired after the conquest of Armenia, which, according to the ŠKZ, opened Šāpur’s second Roman campaign (ŠKZ, Part., l. 4): “and the Caesar lied again, he did harm/sin to Armenia, and We moved into the Roman empire.” The nature of the “harm, sin” (winās) towards Armenia, of which the Romans are accused, is the subject of some controversy. Basing herself primarily upon the Armenian sources, Marie Louise Chaumont suggested that the pretext for Šāpur’s offensive against Rome could be related to the asylum it granted to the young, fugitive, prince Tirdād, son of the Arsacid king of Armenia, Ḵosrow, who appears to have been assassinated at Šāpur’s instigation prior to the Persian invasion. This asylum could then have been interpreted by the Persians as Roman interference in Armenia, which after the treaty of 244 C.E. between Šāpur I and Philip the Arab seems to have belonged to Persia’s sphere of interest, as suggested by the Byzantine chronicler Zonaras (Annales 12.19; Chaumont, 1968, pp. 83-86; idem, 1973, pp. 684-85; idem, 1976, p. 173; also Ensslin, p. 98). Slightly different is the conclusion of E. Kettenhofen, who, after a close scrutiny of the Armenian and classical sources, proposed the year 217 as the beginning of Tirdād’s reign, thereby surmising that Tirdād was, at the time of the Persian invasion of Armenia in 252 c.e., a mature sovereign with a history of 35 years of rule. Furthermore, Kettenhofen seems to subscribe to the opinion that Tirdād’s children sided with the Persian invaders against their father (Kettenhofen, 1982, pp. 38-43; idem, 1995, pp. 56, 140-43; see also Schottky, 1994, pp. 225-32). It is generally agreed that Armenia was annexed in 252 C.E., during the reign of Trebonianus Gallus and the coregency of Volusianus according to Zonaras (Annales 12.21; Chaumont, 1976, p. 172; Ensslin, pp. 18-19; Kettenhofen, 1982, pp. 41, 84; Marquart, 1895, p. 652, places the invasion shortly before 252; so does Rostovtzeff, 1943, p. 33).

Essentially, what one may surmise is that the matter of the Armenian throne is a messy one, both in terms of history and historiography, fraught with irregularities and possibly ideological claims to the crown not matched by political reality. In lieu of anything else, my usual instinct is to go with the conclusions of Touraj Daryaee, which appear to suggest that it was only at some later point that Hormizd was granted the prestigious title "Great King of Armenia".

I think this relates to the original context of your inquiry, regarding Shapur's taking of cities, in that the Armenian situation was not a stable or straightforward one at this point in time.

Sources:

Sasanian Persia by Touraj Daryaee

Encyclopedia Iranica