Was it simply Jecht's bad luck to be where he was that day in the waters? Or was it something more? The fayth constantly repeat that they wish the dreaming to end because they tire of it. And we know that's it's possible for the fayths to interact limitly with the people in their dream Zanarkand. What does this mean?

Since the Bahamut's fayth continually appears to Tidus, I came to the conclusion that he was particularly tied to Tidus -- that Tidus was Bahamut's dream, the one fragment of the last world which was especially his own. Does that necessarily mean that Jecht is also the particular dream of Bahamut's?

I truthfully don't know, but I'd prefer to offer another choice for which Fayth might have dreamed Jecht. For a few reasons, I think that it might be Ifrit's fayth who holds particular control over the dreams which created Jecht. For one, Kilika is the home island of High Summoner Ohalland, which instantly creates a type of connection between star blitzball players and Kilika since Ohalland himself was a great blitzball player; Wakka prays to him for victory when the group visits there. And Jecht -- as everyone knows -- was a star blitzball player. Not the most compelling evidence, but a bit of a connection.

Also, there's a lot of fire imagery connected with Jecht; the colors of his towel/wrap thing and the stylized designs on it which resemble licking flames are indictative of fire. The same design is echoed on his final sword. Then, there's the fire and rocks which surround him in his Aeon-form, both of which are reminscent of Ifrit.

The most compelling evidence, however, is the speech given by Ifrit's fayth if you choose to revisit the temples. While a few of them speak indirectly about Sin and the fayth which became Sin, it is Ifrit's fayth who uses his brief appearence to discuss at length Jecht, how he became Sin and what tragic fate awaits him. His speech:

Sin swam in the sea near Zanarkand.
Perhaps the waking dream eased its suffering.
Your father touched Sin and became real that night, foundering in the seas of Spira.
How sad now that he is caught in the tragic spiral.
He is Sin. He is Lost