How does Cooper end up in Cooper Station after he loses consciousness in the Tesseract?
It seemed quite clear from the film that "they" (whoever set up the tesseract, probably future humans) "dumped" him into space and the present-day humans found him.
As soon as he did what he had to in there, the robot commented that "they" were shutting down that place and soon afterwards Cooper was floating in space.
This is one of a number of homages in Interstellar to 2001: A Space Odyssey.
At the start of the fourth book, 3001: A Final Odyssey, Frank Poole, who was killed by HAL, is found floating in space near Neptune and rescued.
"They" returned Cooper to his own spacetime in a manner such that he would be rescued.