The pattern is very simple.
The basic British rule (as I understand it) is the orthographic "long u" alters the pronunciation of four consonants that preceed it. These consonants are /t d s z/, which become /ch j sh zh/. Almost invariably.
That's the whole rule for the man in the street who pronounces "Tuesday" as "Chewsday".
For the speakers who do not (a distinct minority in the UK), things are a bit more selective: only words of French and Latin origin tend to follow the rule with the orthographic "long u" only in an unaccented syllable. For example: creature, feature, fortune, natural, but not "tutor". (If there is a secondary accent on the syllable, count it as accented.) There are exceptions among these speakers, which may actually be hypercorrections, such as "issue".
In North American English, the consonant shift is the same as the second speaker. The pronunciation of the vowel spelled by the "long u" itself will vary considerably from that of our cousins in the old country, but the consonants will be the same.
As noted by John Lawler, the consonant change is due to an historic intrusive "y" sound. This "y" intruded only slightly in the dialects that formed most North American dialects, thus the vast majority of Americans say /nooz, toon, doolee/ where our cousins would say /nyooz, tyoon, dyooli/ when reading "news, tune, duely".
A similar change takes place with the same consonants when preceding other unaccented "Y + vowel" combinations.