Lilandra gave the Greys a Holoempathic Matrix Crystal with a slightly-shifting image of Jean. It contained the essence and/or personality of Jean herself. When one touched it or held it, they got to see and feel as if Jean was really there with them in person. (I believe each person could get a slightly different vibe off of this.)
There was no Phoenix or Phoenix Force associated with it.
The PF had allowed Rachel access to E-616 and so was there watching when Rachel touched the globe and called out. The PF answered by instilling some of it's power. I know it looks as if it came from the globe, but it did not.*
*Interesting Side Note of my Interest: A snow globe was used in both Carrie original movie and also in remakes and in Carrie 2!