I believe he translated at least some of his works into English himself:
In most cases, Singer published a story in the Yiddish press, and then used tear sheets or clippings to translate it into English.
From The New Yorker
The Smithsonian implies that he did it himself, but sometimes with the help of editors:
He published them first in Yiddish language publications before having them translated or translating them himself with the help of editors into English.
The LA Times also backs up the second Wikipedia quote:
When he later helped translate his own works into English, he cut and changed the text, tightened the narrative and created what he called a "second original."
See also the bibliography found by Mithrandir in chat on the Nobel prize website. It seems to show that he helped with some of his works, that others entirely did the full translation of others, and then Joseph Singer, who seems to be his nephew, helped with yet others.
In yet another fabulous source found by Mithrandir in chat, it says:
During the spring semester, starting in January, he and I taught together a class in creative writing at the University of Miami. On Sundays i came down to his condominium in Surfside, had breakfast with him, and worked with him on his writing - a process described roughly as "translating". The tags at the end of these stories usually read "Translated by the author and Lester Goran" (or some other name over the years, sometimes Singer's wife, Alma, or other times "translated by the author"). It was actually a clerical refinement of transcription more than a literary exercise. He read to the "translator" in English, putting his Yiddish into a form the auditor could understand, and then the translator put the words down into grammatical or, at best, more idiomatic usage.
This is from the fourth page of The Bright Streets of Surfside: The Memoir of a Friendship with Isaac Bashevis Singer (see here for the Google Books copy).
And finally, again from Mithrandir in chat: check the books. While I can't seem to access the ebook version myself, the picture in chat should suffice for proof - it says "Translated by the author and [person]" in multiple spots.
I think the situation is simply that he wrote and published his works first in Yiddish, always (his earlier works were translations of others' work into Yiddish) and then later when his works were better known, he translated his own works with the help of an editor. So while perhaps the Wikipedia article is not ideally worded, there is no true contradiction: Yiddish was the primary language in which he wrote.
This all then of course brings up the question: how much of the translation was him, and how much the editor. One article I found in the Magazine for the National Endowment of the Humanities says
"Translated" is a bit of a misnomer for Singer's work later in his career. Although he continued to write in Yiddish, as he grew more successful, he came to think of the Yiddish originals as templates for the finished English versions. Originally, it arose from necessity; most of his translators did not speak Yiddish. "He sat with them, he would dictate or he would orally translate a version to them in English," says Stavans. "And they would type whatever they had, and then go home to turn it into something more polished. Then they would come back and he would approve it. The result was the English was considered a second original rather than a translation."
(Stavans is referring to "Ilan Stavans, a professor at Amherst College and editor of the Library of America's edition of Singer's complete stories." Wikipedia article on Stavans here.)
which I think is quite enlightening.