clustering plus linear model versus non linear (tree) model
With regards to the end of your question:

So the work team A is doing to cluster the instances, the tree model is is also doing per se - because segmentation is embedded in tree models.
Does this explanation make sense?

Yes, I believe this is a reasonable summary. I wouldn't say the segmentation is "embedded" in the models but a necessary step in how these models operate, since they attempt to find points in the variables where we can create "pure clusters" after data follows the tree down to a given split.

Is it correct to infer that the approach of group B is less demanding in terms of time? (i.e. the model finds the attributes to segment the data as opposed to selecting the attributes manually)

I would imagine that relying on the tree implementation to derive your rules would be faster and less error prone than manual testing, yes.