I thought Morrison's New X-Men was great. It was one of the most creative, witty, and intelligent X-Men runs. It had themes and subtexts running through out it (tearing through self deceptions, new v. old, post-humanism, mutant culture etc).
Anyways Here Comes Tomorrow was a possible future that had the same history as 616 up until New 150 and it was the real 616 Jean that woke up in the HCT future and then cut it away from the White Hot Room.
It always amazes me how fans didn't know that the White Hot Room existed in continuity before Morrison's run. He only named it, added the Phoenix Corp, and officially put it in the M'Kraan Crystal.
The WHR is the same place as Claremont had Jean go as White Phoenix in Classic 43. Its a space like realm with floating towers. When beings die they go to the afterlife and exist in the towers. The Phoenix exists outside the towers to "craft her chaos from without and within".
Claremont had also established that there was a White City inside the M'Kraan Crystal. When he had Jean heal the M'Kraan Crystal she felt connected to it.
So Morrison just combined these concepts and added some of his own spin. Like I said Jean being a White Phoenix and there being a Phoenix Consciousness also came from previously continuity.
The sad thing was that a lot of fans didn't know that.
Morrisons version of the Phoenix really streamlined it. He salvaged the original continuity (that Jean was Phoenix and its apart of her mutation), put the Classic X-Men backstories back in continuity, and used many of the retcon elements (other Phoenixes, Phoenix Consciousness, cocoon (now Phoenix Egg), replacements (now not literal, just being consumed by the Phoenix).
Its Simple. Lets take Jean for example.
Jean has a mutation that makes her a Phoenix. She is connected to the Phoenix Consciousness that tries to compel her to burn away what doesn't work. When she dies she either instantly resurrects or goes to the White Hot Room to do Phoenix Work and return later through a Phoenix Egg.