The basis varies depends on the magic. Mab's Unseelie Magic might be drawing on her realm or her mother or her own mantle or just nebulous greatness. The Merlin's ward magic might be getting it as a free extra for extreme expertise or burning a bit of his human soul or incurring some karmic debt.
Debt doesn't have to mean anything in-character because FP don't exist in-character. So the justification can be more or less anything.
Except that debt DOES mean something in character with Sponsored Magic (as I've pointed out before, just like Fate Points do mean something in character) and "self-sponsored" magic just borrowed the template seemingly without considering the narrative consequences. But I've pretty much gone over all of this before and really what it comes down to is that you think that agenda-related and other debt are the same thing, while I profusely disagree for reasons I've already stated.
And you can potentially justify the debt, sure, but Sponsored Magic has a single reason for all sponsored debt.
Since you mentioned the subject of Mab, she doesn't HAVE Unseelie Magic. She has "plot device-level magic" (per Our World). Whether it comes from Mab, the Mantle, Mother Winter or the abstract concept of Winter itself Unseelie Magic is something that only characters borrowing that power can have because its Sponsored Magic.
One of my problems then, is that "self-sponsored" magic borrowed this concept but didn't have a reason for it across the board other than that it was part of the Sponsored Magic template.
I don't know what this is supposed to mean, exactly.
Not really sure what got lost in translation. The FATE system is built on a narrative structure. When you read a book (Hero's Journey aside) typically the character is good at certain things (Skills) and most of the time she's going to succeed at what she's good at and fail at what she's not. Of course, its a game so we don't want the results to always be predetermined so we use the FUDGE dice, which only
average 0. Typically when the hero DOES succeed or fail where she shouldn't its because of something in her background (Aspects). The hero usually gets beat up at the beginning (Compels) and fantastically outdoes all previous conceptions at the end (Invokes).
So... when you make a mechanic in FATE, you make it support the narrative. If it doesn't support the narrative (it doesn't fit or it doesn't have a compelling reason to exist) then its a bad mechanic (aside: This is why I don't think Soulfire is actually Sponsored Magic no matter what the RAW says).
For the sake of saving some argument, let me give a try at making what you want in a way that I would consider to be at least
less problematic.
Excessive Specialization [-1]For some reason, you've abandoned the traditional path of magical study. Maybe you never had a mentor. Maybe you're on the run from the White Council. Or maybe you're Mommy just always told you you were a unique little snowflake and you're going to be and to heck with the consequences.
Musts: You must have an Aspect which alludes to this ability (typically your High Concept)
Each time you take this, you must choose a field of magical study (eg: Ectomancy, Demonology). If you have taken both Ritual and Channeling in the same field you get a one-time refund of 1 refresh when you take this power. You may take this ability multiple times. It may not be applied to a category of magic (Warding, Summoning and Binding, Crafting).
*
Just That Good. You gain +1 to Control OR Complexity and Power OR Strength and Frequency when dealing with magic in this field.
This ability may only be taken once per field, not once per bonus type. This bonus stacks with itself and specializations. Control applies to both Thaumaturgy and Evocation magics.*
Combat Casting. You may cast relevant Thaumaturgic rituals at combat speed provided you draw all the necessary power in one exchange. You may take this ability once per field.
*
True Ritual. You may use one of your rote slots for a relevant Thaumaturgic ritual. The Thaumaturgic rote automatically succeeds after a number of exchanges (min. 1) equal to the complexity of the spell minus your Control.
All parameters (except target, unless the target is yourself) and including any bonuses from foci and the source of any extra shifts for complexity must be set when this power is taken. This ability may be taken once, plus one for any slots Rote Caster gives you. This ability may be combined with Combat Casting provided the rote takes one exchange.*
Rote Caster. You have gain a number of rote spell slots equal to your Lore that must be used for Rotes in the field of study.
*
Easy Peasy. You may cast a single relevant rote for one less stress (min. 0) than it would normally take. You may take this ability once per rote.
*
Of Course I Know That. You automatically succeed at any knowledge roll relevant to casting of spells in this field (eg: internal anatomy for Biomancy) provided the difficulty is less than your Lore.
I realize those abilities are kind of all over the map (and the refresh cost may be off because of it), but this basically reflects most of the things you'd want a specialist to be able to do generically without taking on any extra baggage.
EDIT: Added a couple clarifications including that bonus is +1 to Control for Thaumaturgy and Evocation OR a +1 to Complexity and Power.