Martial base classes each have their own separate initiator level, just as spellcasting classes have their own separate caster levels, psionic classes have their own separate manifester levels, and so on. Unlike those other cases, however, initiator level includes half your level in other classes – including other initiating classes.
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. Look up the result on the table below to determine
the highest-level maneuvers you can take. You still have to
meet a maneuver’s prerequisite to learn it.
For example, a 7th-level crusader/5th-level swordsage
has an initiator level of 9th for determining the highest-
level maneuvers he can take as a crusader. As a result, he
can take 5th-level crusader maneuvers. As a swordsage, his
initiator level is 8th, allowing him to take 4th-level sword-
This process applies to all of a character’s levels, whether
they are in martial adept classes or other classes.
Prestige classes work a little differently. In most cases, you
add the full prestige class level to your martial adept level to
determine your initiator level. See the prestige class descriptions in Chapter 5 for details.
(Tome of Battle pg. 39, emphasis mine)
Clearly, the Crusader 7/Swordsage 5 example is quite similar to your Swordsage 13/Warblade 2, so clearly at 15th level you had a swordsage IL of 14 (13 + ½×2) and a warblade IL of 8 (½×13 + 2).
As it says right there at the end, prestige classes are a little different, mostly in that “you add the full prestige class level to your martial adept level to determine your initiator level.” This means the five levels of master of the nine counts for both swordsage and warblade, for ILs of 19 and 13, respectively.
The mention in the prestige class section defines how learning maneuvers and getting more maneuvers readied works. It does not directly address initiator level, however.
Advancing Martial Progression
If you have levels in a martial adept standard class (crusader,
swordsage, or warblade), you retain the same method for
readying and recovering maneuvers that you previously
used. If you have levels in two or more martial adept standard
classes (for example, you are a multiclass swordsage/warblade), you must decide to which of your existing martial
adept classes the new maneuvers known or maneuvers
(Tome of Battle pg. 96, emphasis mine)
Note that you choose which existing class gets the new maneuvers known or readied, not the initiator level.
Master of the nine simply repeats what was said on page 39:
You add your full master
of nine levels to your initiator level to determine your total
initiator level and your highest-level maneuvers known.
(Tome of Battle pg. 119)
Since Tome of Battle only ever says that you simply go ahead and add prestige class levels in full to initiator level, this has been interpreted, universally that I have seen, to simply do exactly that: add on to any and all initiator levels you have. Nothing in Tome of Battle ever says that you must choose which class to add prestige class levels to, as every spellcasting prestige class does.