Disillusioned JW, the link you provided to the Cista Mystica website is no longer accessible, but I was able to access the same material here. It maintains that the term 'christian' does not occur until codex Alexandrinus, which it suggests may be later than the 5th century C.E., and that prior to this the term 'chrestian' was invariably used.
However, P72 (also known as P.Bodmer.VIII) is a manuscript dated to the third or fourth century which contains the two letters of Peter. At 1 Peter 4:16 he writes "But if he suffers as a Christian, let him not feel shame ..." and P72 renders this as "ei de xristianos me eschunestho", so it is not true that the term 'christian' only occurred much later. You can actually see the manuscript on the Vatican Library website here, with 1 Peter 4:16 at the top of p.19.
Why then, is there early use of the term xrestianos? In the book Lettered Christians: Christians, Letters, and Late Antique Oxyrhynchus, 2012, by Lincoln H. Blumell he explains (p.37):
While the epithet "Christian" certainly appears to have been derived from the word "Christ", to an outsider who might not have been necessarily familiar with the association [of Christians] it sometimes appears that it was taken to have an association with the adjective xrestos (good) ... it is not always clear if such a distinction is being made consciously or whether it is simply a mispronunciation.