It is known that there are various account on what happened in Nibelheim. The scene where Sephiroth falls into the Mako stream in the reactor was different. In the original FFVII,
Sephiroth stabbed Cloud, but Cloud overpowered Sephiroth, lifted the latter and throw him into the Mako stream below. In another adaptation (forget which one), Sephiroth gladly throw himself into the Mako stream.
This could possibly because the scene in the game was based on Cloud's memory, thus it might be a bit hazy. In other words, he might not remember it correctly (the game version of the story).
Although the 77,777 copies of Advent Pieces: Limited that were released in Japan sold out months in advance of the official release date, Last Order received a negative fan response due to changes in content and presentation from the original Final Fantasy VII game, and because of this, the crew working on Crisis Core avoided recreating certain scenes from Last Order.
As for why Tifa doesn't remember that Cloud went to Nibleheim, in the game she was unconscious and the Soldier member that was dispatched to Nibelheim was Sephiroth
and Zack. Cloud was a Shinra Trooper and he didn't take off his helmet, so Tifa was unable to recognize him.