Why Tournaments are Ordered
Unlike some other rating systems, in the ICU system a player's start rating in a tournament is from the last tournament the player competed in and not from the most recently published rating list. To facilitate this, all ICU rated tournaments are put in order so that every tournament (except the first) has a predecessor.
Thus the start rating of a player in tournament number 100 is obtained from tournament 99, or if the player didn't play in 99, then from 98 and so on until the last tournament the player competed in is found or, if none can be found, the player has no start rating.
The Old System
In the old ICU system (pre-2012) this ordering, in theory at least, was based mainly on tournament start date (augmented with some tie-breaking criteria). However, in practice this order couldn't always be adhered to because of tournaments that were submitted late or which took a long time to finish. The main difficulty was the amount of work involved in producing revised lists and this was coupled with the desire to avoid altering published ratings.
For example, a tournament played in November but not reported until March would have been placed in the earliest available slot just after the January rating list (for rating in May) even though in theory (if tournaments had been reordered) it should really have contributed to a recomputed January list.
The New System
In the new rating system (this web site) the problem has been curtailed by adopting a different ordering rule, one based on tournament end date rather than start date. Thus the Leinster leagues, for example, which take several months to complete, are ordered based on an end date sometime in April (rather than a start date in October) and therefore contribute to the rating list in May and can be rated in their proper order without affecting the January list.
Late reported tournaments still present a difficulty, however. The new rating system automates the reordering and rerating of tournaments and republication of rating lists, so the risk of introducing new errors while recalculating old rating lists (a long and partially manual task in the old system) has been eliminated. However, it's still unsetting for players when their ratings suddenly change without explanation.
To cope with late tournaments and other kinds of corrections the new system introduces the concept of original published ratings. Please see the relevant article for further details on this.