While it's pretty clear that all your different non-martial adept classes count for your Initiator Level, regardless of the order, this line:
If you are a multiclass martial adept, and you learn a new maneuver by attaining a new level in a martial adept class, determine your initiator level
does make it seem, rules-as-written, as if your Initiator Level is only checked and updated when you take a new level in a martial adept class, I think other parts of this section make it clear that this is not the intention:
INITIATOR LEVEL: Some maneuvers and stances have variable effects (such as duration) that depend on initiator level ... If you lack any
martial adept levels, your initiator level is equal to 1/2 your character level.
- p.39 Tome of Battle
This section makes it clear that you have an initiator level, even if you lack any martial adept levels. This suggests that there is nothing special about taking a martial adept level that updates your Initiator Level.
MULTICLASS CHARACTERS: Even when you gain levels in a class that does not grant martial maneuvers, your understanding of the martial
disciplines still increases ...
If you are a multiclass martial adept, and you learn a new maneuver by attaining a new level in a martial adept class, determine your initiator level by adding together your level in that class + 1/2 your levels in all other classes ...
This process applies to all of a character’s levels, whether they are in martial adept classes or other classes.
- p.39 Tome of Battle
Broader context in the multi-class characters section suggest that the awkward wording of the quoted sentence is not meant to put any directionality on gaining Initiator Levels. Right after describing the process of calculating Initiator Level when multiclassing, they state that "this process applies to all of a character’s levels, whether they are in martial adept classes or other classes", which, I think, is a clear argument that we should update Initiator Level each time you level, not just if the level is in a martial adept class.