There may be a difference between what an author writes as "ai" versus "aj", but this is usually a substitute for the difference between a sequence of vowels in different syllables versus a vowel plus high front vocoid in the same syllable. The difference could be written as [ai] versus [a.i], but writing syllable boundaries is not a popular option especially in a practical orthography.
There actually is a phonetic difference in North Saami between [u:C] (=[uuC]) and [uwC], which is auditorily very elusive, which is realized in subtle low-level differences in fricative noise in the case of [w] before certain consonants. In your case, the author seems to be saying something about low-level phonetics, and really there is no substitute for listening to examples – which isn't possible in this case. I would expect the duration of the [uj]-transcribed token to have a shorter duration on the palatal segment, compared to a token transcribed with [ui]. Generally, [j] has a much shorter duration compared to [i], also the constriction is often greater. He makes a similar statement about iu and tone two pages before – perhaps there is some phonetic study of the difference in Mandarin. I would expect the difference to be about duration.