Disillusioned JW : The site mentioned above says (and shows) that the Codex Sinaiticus, the Codex Vaticanus, and the Codex Beza each say "The disciples were first called Chreistians in Antioch ..."
Interestingly, these codices do not all read the same. Codex Sinaiticus reads chrestian in the three places the word "christian(s)" occurs (Acts 11:26; 26:28; 1 Peter 4:16). But codex Vaticanus and codex Bezae read chreistian, and codex Alexandrinus reads christian. All three words sound much the same but there was obviously some confusion about the term used.
Harnack discusses the use of chrestians by Tacitus in his Mission and Expansion of Christianity, pp.410-414
We now come to the name "Christians," which became the cardinal title of the faith. The Roman authorities certainly employed it from the days of Trajan downwards (cp. Pliny and the rescripts, the "cognitiones de Christianis"), and probably even forty or fifty years earlier (1 Pet. iv.16; Tacitus), whilst it was by this name that the adherents of the new religion were known among the common people (Tacitus; cp. also the well-known passage in Suetonius).
A word in closing on the well-known passage from Tacitus (Annal., xv. 44) ... Hitherto, however, the statement of Tacitus has appeared rather unintelligible, for he begins by ascribing the appellation of "Christians" to the common people, and then goes on to relate that the author of the name was Christ, in which case the common people did a very obvious and natural thing when they called Christ's followers "Christians." Why, then, does Tacitus single out the appellation of "Christian" as a popular epithet? ... in my judgment the enigma has now been solved by means of a fresh collation of the Tacitus MS. which shows, as I am convinced from the facsimile, that the original reading was "Chrestianos," and that this was subsequently corrected (though "Christus" and not "Chrestus" is the term employed ad loc.). This clears up the whole matter. The populace, as Tacitus says, called this sect "Chrestiani," while he himself is better informed (like Pliny, who also writes "Christian"), and silently corrects the mistake in the spelling of the names, by accurately designating its author as "Christus". Blass had anticipated this solution by a conjecture of his own in the passage under discussion, and the event has proved that he was correct.
My conclusion is that while they were initially called "christians" at Acts 11:26, as the expression became common others who heard it adapted it to "chrestions" as they misheard and didn't understand the origin of the term. If the writer of Acts had used any term other than "christians", it would not have made sense that the appellation was "by divine providence".