my 3rd(?) edition books require multi-discipline adepts to perform separate karma rituals, and track their karma separately for each discipline (note: you still only get one ritual per day, and it only refills one discipline. and of course, you paid for each point of karma back then in legend points). it also had optional rules requiring the purchasing of separate karma ritual talents and being unable to spend karma from one discipline on talents from the other. they also talk about how you almost have to change your entire perspective between your disciplines to effectively use them.
as far as 4th edition is concerned, i suspect the goal would have been to simplify this. but at least in earlier editions, it appears that the intent was that you do your karma rituals separately for each discipline, and potentially that you track and use karma for each discipline separately.
in contrast, here's what i've got in my 4th edition book on karma rituals (player's guide page 83)
"Each Discipline includes a sample ritual that allows characters of that Discipline
to regain Karma Points. The player need not make any tests to perform the Karma
Ritual; it is always successful. Your character may perform his Karma Ritual once each
day, and the ritual takes about half an hour to perform. After he performs his Karma
Ritual, all of his Karma Points are restored. A character’s maximum Karma is determined
by his highest Discipline Circle, multiplied by the Karma Modifier for his race.
For example, a Third Circle human adept has 15 maximum Karma Points.
While there are many similarities between the rituals practiced by adepts of the
same Discipline, every Karma Ritual is unique. Individuals will adapt their ritual to
fit their personal vision for the Discipline. Players are encouraged to create unique
Karma Rituals for their characters."
and (page 459, advancing in a new discipline - karma)
If multiple Disciplines grant the ability to spend Karma on a particular kind of
test, the character may only spend one Karma Point using that ability. For example,
a Fifth Circle Air Sailor who is also a Third Circle Swordmaster may only spend one
point using the ability to spend Karma on Interaction tests. Unless a rule description
specifically says otherwise, this applies to any talents or duplicate abilities."
so yeah, much more simplified. one pool for all disciplines, based on the highest discipline. in this spirit, i'd say you could likely perform either karma ritual and receive the same benefit, and i would go even further and suggest that your ritual (being slightly different from others) is likely have *some* reflection of your other disciplines in them. with the only restriction being that you don't get to double-dip on spending karma.
hope that helps