The source of the quote is John J. O'Neill's Prodigal Genius: The Life of Nikola Tesla (1944). The story essentially claims what The Oatmeal says: that Tesla went so far as to see machines built with his improved parts before Edison denied him his money.
There, I am afraid, the trail ends. O'Neill was a Pulitzer Prize-winning journalist, but he did not explain where he heard this particular quote.
This is what Tesla himself had to say:
For nearly a year my regular hours were from 10:30 a.m. until 5:00 a.m. the next morning without a day's exception. Edison said to me, "I have had many hard-working assistants but you take the cake." During this period I designed twenty-four different types of standard machines with short cores and of uniform pattern which replaced the old ones. The Manager had promised me $50,000 on the completion of this task but it turned out to be a practical joke. This gave me a painful shock and I resigned my position.
The footnoted counterpoint that you offer in the question is apparently dubious. (see following source) But it should be noted as well that there is evidence Tesla was embellishing his own autobiography. He worked for Edison for six months, which is not "nearly a year," and the direct cause for Tesla's resignation was not this incident but rather when Edison tabled another invention of his, in favor of making a mutually beneficial business deal with another company instead. (source and details)
So this boils down to precisely what Reddit says it does. It's Tesla's word against the word of Edison's supporters, and O'Neill's biography is responsible for making Edison himself the villain. We can no longer know today what actually happened between Tesla and "the manager" or who "the manager" really was.
In the 1940s it was entirely common to embellish on stories you read elsewhere, even when writing non-fiction biographies. I think it is plausible to say that O'Neill took Tesla's story and misread it in a way beneficial to imagining Tesla and Edison as direct rivals. Samuel Insull is a likely better candidate for the manager.