When did the phrase begin?
Who started it?
Dr Dre, apparently.
Dre’s album but I think that was Snoop Dogg making the call on the album.
I’ve never seen it written as Deetz Nuts, and on the album it’s actually “Deeez Nuuuts”.
Perhaps you ran across Dietz Nuts which seems like it would share the pronunciation of the OP’s spelling. They are the result of the deli meat supplier, Dietz and Watson, having a little fun with the phrase (trademarked well after the Dre album). They aren’t even actual nuts.
In 2015, a fifteen-year-old from Iowa filed with the Federal Election Commission as a candidate for the U.S. Presidency, under the pseudonym “Deez Nutz” (undoubtedly borrowed from the song), and generated a fair amount of publicity (and actually getting a non-zero amount of “support” in polls), undoubtedly due to the silly name.
And for anyone wondering, it was originally a little skit between songs on the classic rap album “The Chronic.” Snoop Doggy Dogg (as he was then known) calls up a young lady and says, “Hey did, uh, wass-his-name get at you yesterday?” She replies, “Who?” To which Snoop hits her back with “Deeeez nuuuuts!”
And a meme was born.