RSo,
No that is not how I understand it. I understand it as meaning that the tzadik doesn’t leave this world, rather he is found, in addition, in the other three worlds. That’s how the Alter Rebbe understands it and explains it in Tanya, igeres hakodesh, epistle 27, and I rely on his kabbalistic knowledge. I don’t presume to have any understanding of any of these kabbalistic inyanim of my own (that would be highly intellectually dishonest and irresponsible, as I do not claim to have the ability to reach an understanding of these inyanim on my own.) Rather I rely on the Rebbeim to guide me in my understanding of it.
However you asked where the source of the idea comes from, and I provided the source.