The other night before bed I tried Xanth's method for phasing, and I had some very interesting and amazing results, not sure if it was quite phasing though. So, I tried all the visualizing and the noticing and all that stuff, and it seemed like quite a bit of time passed, and all of a sudden I was in a dream that i still remember very well, not long into it I became lucid and it ended after what seemed like probably a minute. So at this point I was semi-awake and thought let's try this again. Soon after that, the same thing happened, I was in a different dream setting and became lucid very quickly, but this time right when i became lucid it seemed like everything slowed down for a second and then I started floating up and down very fast and would settle at a different environmental setting, this happened 3 times before i lost it and again kind of woke up. I tried it once more and again was in a dream setting in which i became lucid very quickly but it was over fast and I don't really remember any of it. After the third lucid dream, i woke up completely and looked at my alarm clock and less than an hour had gone by since I started this process. So to get one thing straight, I have never ever had lucid dreams like this right after going to bed, let alone have then back to back to back. It almost seemed like I just was in the zone that night or something lol, I tried it the next couple days but nothing happened. I'm pretty sure it was some form of phasing but I was never aware right off the get go.
From your description... you fell asleep as normal and started off with a dream awareness (a normal dream)... to which you gained lucid awareness shortly thereafter. :)
For myself... to call an experience "phasing", you go from the physical being fully aware directly into the non-physical being fully aware. There should be no point along that where you have a dream awareness. If that makes any sense.
But you were close! VERY close...
In the end though, you DID have a conscious non-physical experience, so that's really all that matters. :)