Cross's story is the same in Dreamswap, except that he was abandoned by ds ink in the void and met with ds nightmare. And had to learn to control X Chara. He wouldn't of been surprised by his own backstory before the point of Ink in Underverse meeting him and the drama starting.
While DS!Cross’ story is extremely similar to his original’s, there are still many differences. For example, XGaster’s mindset when he was overwriting the story was similar to that of a fanfiction author’s.
fun fact, Nightmare met XGaster when he was dying, but Nightmare refused to do anything and left his soul, which Dream later found and took to the JR storage.