Why do 2 of the tree peonies I purchased have herbaceous Peony emerging From the ground in the spring? If left to flower it forms a simple magenta colored boom, unlike the tree peony's bloom. Is this part of the propagation of tree peonies ?

Tree peonies are grafted - if your peony came in a pot, the graft was buried a few inches underground so you never saw it. What you are seeing are shoots from the herbaceous root stock peony. Remove them but, make sure its a herbaceous peony stem and not a new shoot from the tree peony roots. Given time, the tree part will develop its own root system but the herbaceous roots will always be there.

This page has a super guide with pictures on both why it happens and what to do about it. Realized mine was probably planted too shallow.
www.treepeony.com/pages/herbaceous-understock-sprouted-on-tree-peonies-part-i