Reincarnation and Simultaneous Time / Multidimensional Reality
Theoretical physics has caused many to change their views how reality works. Conventional ideas view time as linear with the every changing present moment-point being the only thing that is "real". Taking the multidimensional aspects of reality into consideration, time takes on a simultaneous nature with probables pasts, probable futures and alternate/parallel presents all existing "now" simultaneously. Our linear sequential view of time is only due to our changing perspective as a part of the physical portion of reality.
What the children in this show are experiencing is a bleed through from a portion of their psyche that has a relationship to a part of themselves that is "living" "now" in another time. Reincarnation is not living one life, then living another until all the karma is worked out. Each individual persons life and identity is unique. Upon physical death most decide to experience more lives focused in the physical aspect of reality. This is more like planting a seed to create a new individual and assisting them with their lives, learning new lessons as they do. The original identity is never lost. "You" will always retain your individual personality. In addition, reincarnational lives can be chosen in the past, as well as the future. So, you can have multiple lives simultaneously in different times. These are related, but each is a new individual.
If any of you are interested in this line of thinking, I suggest you read any of the books by Jane Roberts / Seth.