The Purdue Online Writing Lab, which claims to follow APA style, gives this example that seems to match your example (except that it concludes with a period rather than a comma):
Additional Punctuation Rules When Using Quotation Marks
Put commas and periods within quotation marks, except when a parenthetical reference follows.
[Relevant example:] Mullen, criticizing the apparent inaction, writes, "Donahue's policy was to do nothing" (24).
It seems clear to me that the same rule would give you this example if the sentence continued after the parenthetical, separated by a comma:
Mullen, criticizing the apparent inaction, writes, "Donahue's policy was to do nothing" (24), though Mullen is rather fuzzy about what affirmative policy would have worked better.
APA itself provides this relevant example from a sample one-experiment paper (in PDF form) linked to its site:
However, despite the preservation of emotion-processing regions with age (or perhaps because of the contrast between the preservation of these regions and age-related declines in cognitive-processing regions; Good et al., 2001; Hedden & Gabrieli, 2004; Ohnishi, Matsuda, Tabira, Asada, & Uno, 2001; Raz, 2000; West, 1996), recent behavioral research has revealed changes that occur with aging in the regulation and processing of emotion.
Note that the comma falls after "1996)" and not after "age" many words earlier.
From these guidelines and examples, it follows that the version of your original sentence that is more in line with APA style is the first of the two you offer above:
In my reading, when I came across “fairmindedness” (Paul & Elder, 2012), I automatically thought ‘yes, I am fair-minded.’
I suspect, though, that APA would also prefer double quotation marks around the phrase "yes, I am fair-minded."