Shinji and Asuka did not travel back in time due to their wish, but thanks to the The Alpha Numbers or the the Z.E.U.T.H. crewYes, really. The Super Robot Wars heroes are -much to their personal disgust- acquainted with time and interdimensional travel. Several characters from the original series have several versions of them (such like Kouji Kabuto or Ryoma Nagare), or have crossed into other dimensions (Show Zama, again Ryoma Nagare). Kouji Kabuto himself has been stuck into a Groundhog Peggy Sue situation in one of their series (and bits of official material hint the Gundam universe itself and all Yoshiyuki Tomino series form a gigantic Ground Hog Peggy Sue cycle). So they accidentally landed in the post-Third Impact, original timeline we saw in the flashbacks episodes, they easily deduced what had happened (the cruxified MP Evas and Rei's giant head would be a deadly giveaway to Shinji, Asuka and Rei) and they decided fixing it. So Kouji, Tetsuya, Duke, the Getter team, Hiroshi, Akira, the Combattler team, the Voltes team, Kazuya, Sanshiro, the Zambot team, Banjo, Amuro, Char, Camille, Juudau, Hikaru, Noriko, Guy, the counterparts of Shinji, Asuka and Rei of the Super Robot Wars universe... tracked someone -Kaworu or whoever he answered to- powerful enough to correct things (there are several possible ways how they could have managed this: Shin Getter Robot is a hugely powerful sentient mecha is quite willing acting on its own (much like Mazinkaiser) and is powered by a sentient form of energy controls and manipulates evolution (the Getter rays), and how it was seen in Super Robot Wars Alpha, Instrumentality is NOT the direction the Getter rays want humanity going towards; Ideon and Raideen are sentient, divine mechas, and Rei is partially Lilith) and they kicked its butt to convince it into giving that dimension a new chance. Then Kaworu agreed to send the Ikaris back in time (something he was going to do anyways), and he did so when Shinji and Asuka wished for a better life for their daughter. He never mentioned all of this to Shinji why he did wish not trouble him with tales of people from other world (and because he did not want to admit alternate Asuka had threatened him with grievous bodily harm if he ever approached Shinji).
Shinji and Asuka traveling back in time was the Plan B.Whoever was behind the Angels attacks did not intend to exterminate the humankind or merging all human souls in a single being, but testing them (a trial SEELE caused and set off when they awoke Adam). When the Children failed on saving humankind, the plan changed to let Shinji and Asuka survive for a while on that lonely world to show them the consequences of their failure and what The End of the World as We Know It really means, and then sending them back in time properly motivated to prevent Instrumentality. If they won this time around, they would have their daughter back, and a chance for a normal like in return.