The citation given by these sources is insufficient to locate the quote, and a less careful person would conclude it was fabricated, but with a little online research I discovered the following: "The Jerusalem Talmud (y. Ber.2.4*) comments, ‘... King Messiah is born...he is from the royal palace of Bethlehem.’"… "*As cited in Alfred Edersheim, Life and Times of Jesus the Messiah (Hendrickson edition, 1993) p. 143, who says that ‘in an imaginary conversation between an Arab and a Jew, Bethlehem is authoritatively named as Messiah's birthplace.’" (jewsforjesus.org/publications/issues/16_09/predictions, though the phraseology quoted from the Talmud is not supplied by Edersheim and it seems as though an intermediary source may have been utilized.) The "5a" in the earlier citations, appears in Edersheim as a qualification of the 2:4 in the latter. The earlier citations omitted a detail which placed the quote significantly later than what they implied. In fact, this narrative from chapter 2:4 falls out on page 25b when the pages are enumerated from the beginning.
"In the fifth chapter of his book, Micha records one of the most specific predictions about the coming Messiah. His birth place was to be in an obscure village in the province of Judea in Palestine; the city that King David had been born in, Bethlehem" Hal Lindsey, The Promise, page 58. "Some of the most important prophecies about Christ accurately predicted [his] birthplace (Mal. 5:2)" Dan Story, Defending Your Faith, page 78. "The Hebrew scriptures accurately foretold hundreds of years in advance that this Promised One would be born in Bethlehem….Michah 5:2) Watch Tower Bible and Tract Society, You Can Live Forever in Paradise on Earth, page 56. "We must not be confused by all these places and deem them contradictory, for all were touched by [him] in the course of [his] divinely planned life. As Michah prophesied, Jesus was born in Bethlehem…" Herbert Lockyer, All the Messianic Prophecies of the Bible, page 64. "Micah named the place where Christ was to be born seven hundred years before [he] was born there." J. Vernon McGee, Thru The Bible with J. Vernon McGee vol. 3 page 790. "Micah 5:2…Since Micah lived in the time of King Hezekiah, he made this prophecy some eight centuries before Jesus." Islam Revealed, Dr. Anis A. Shorrosh, page 122.
[2 ] I would like to again highlight our earlier citation “We must not be confused by all these places and deem them contradictory, for all were touched by [him] in the course of [his] divinely planned life. As Michah prophesied, Jesus was born in
 While I have not extensively reviewed the question, it is noteworthy that the Watchtower publication cited above does not mention this interpretation of Michah 5:1, nor does Yirmeyahu Ben David. Both reject the traditional conception of the Trinity and the divinity of the Messiah.