Indeed, thanks AnomalousMonk, that was poor wording on my part. I should have added an "in this case" or something similar at the end since I meant that statement to apply to the specific alternatives being checked for a match against the specific string given, not a general statement to say "the order of such alternatives never matters". I do go on to explain it checks the leftmost alternative first.

For some reason I originally thought it would drag the first (leftmost) alternative through the entire string before trying the second alternative and so on. Probably a silly thing to have ever thought, especially when considering groups of alternatives contained within more complicated regular expressions.