The supernatural ability aspect of healing possessed by the prestige class Singer of Concordance (Races of the Dragon 91-6) is unclear as to how it's supposed to function. No errata nor Sage Advice discusses the ability. The DM must rule what, exactly, the aspect of healing affects.
House Rules
However, were a Singer of Concordance present in my campaign, unless a compelling case was made otherwise, I'd likely rule that to benefit from the aspect of healing, the healing must be performed—that is, a creature must have taken some kind of action for the aspect's effect to be realized. Hence, I'd allow a creature that, for example, took a standard action to drink a potion of cure light wounds to benefit from the aspect as I would a creature that took a swift action to activate a cloak of predatory vigor (MIC 87), but I would disallow the benefit to extend to, for example, a creature possessing a natural, constant source of fast healing.1
In the case of spells like the 1st-level Clr spell lesser vigor [conj] (Spell Compendium 229), I'd let the initial effect benefit from the aspect—the spell healing an additional 1d8 points of damage and granting fast healing—but the remaining duration would grant only fast healing at the spell's printed rate with no increase from the aspect.
1 That's not because such an effect would be particularly powerful—the typical Singer by the time the aspect of healing's gained is, after all, usually level 11 and can cast heal, for Io's sake!—but simply because that's how I'm reading the limits of the aspect. Your mileage, as always, may vary.