You are correct in assuming that Jecht is also a Dream, but, in FFX, the term "Dream" is deceptive. Tidus, Jecht, and the other residents of Dream Zanarkand are Dreams of the Fayth in that they are given substance by that Dreaming. In other words, Tidus and Jecht, and Dream Zanarkand itself, are only dreams in the sense that their reality is necessarily manifested by Yu Yevon's Summoning, invoking the Dreaming of the Fayth. If that Dreaming ends (as it did at the end of the game), the link that Dream Zanrakand's populace has to Spira is removed, and their souls travel to the Farplane (in other words, they die).Originally Posted by Kamrusepas
In this way, it can be understood that Tidus and Jecht are not "dreams" in the conventional sense. In being Summoned, they're actually more akin to Aeons. In any case, Jecht had real physical presence (a physical reality substantiated by the process of Dreaming), and thus could interact with Spira in a physical way. Ultimately, he was used for Braska's Final Aeon. At the point that the Aeon pierced Sin, Yu Yevon possessed it, as it would provide the next "anchoring point" for the pyreflies that ultimately comprise Sin. From within, Yu Yevon would continue his fateful Summoning of the Dreams of the Fayth.
However, Tidus and the others did not defeat Sin in the conventional manner (using the Final Aeon, which necessarily perpetuates Sin). Rather, they actually defeated Yu Yevon. In destroying the progenitor of the Summoning/Dreaming, the Dreaming stopped, and Tidus lost his physical link to Spira.
In conclusion, the party did not spend the entirety of the game fighting a figment of the imagination. Rather, they fought an entity whose "core" was physically manifested by the very concept it helped to perpetuate.