My question I guess is how the selection is done. A brief explanation with a simple access tree will be very helpful.
I suggest, you look into the code how that works. Basically, you start with a secret that you want to share according to some tree. You share the secret with a Threshold Secret Sharing Scheme like Shamir's Secret Sharing and put the resulting shares into the children of that node (in the beginning this is the root node). Then you can re-share each of the shares if this is necessary. Here is an example:
In the end, every non-leaf node in the tree has its own polynomial that has to be evaluated and every leaf node has a share. In the reconstruction phase, you apply Lagrange interpolation at each node from the bottom up.
Of course, it is possible to make some optimizations. For example, if the root node is an OR gate and the left subtree is large, but the right subtree is only a single leaf, then you should first check whether the right subtree is satisfied and reconstruct the root secret only from one leaf.