Conceptually, yes that is how BackboneFast is supposed to work. Which debug are you running here? Looks like debug spanning-tree events. I don't think this shows you the RLQ messages. Can you try the same thing with a debug spanning-tree backbonefast?
I have run the debug "spanning-tree backbonefast" as well but not luck. Also the port transitions to LIS/LRN state only after the expiry of Max-Age timer.
Sorry about the late response. I tested this out myself and I see the same behavior that you do. It looks like BackboneFast is supposed to kick in only in cases of indirect root failure.
It seems to be looking at the root bridge information only to determine if a BPDU is inferior or not. An inferior BPDU due to a higher cost to root does not cause it to run. With a path cost increase only, the root bridge information still remains the same. So a switch receiving such a BPDU already knows that the root is not lost, only the cost has changed.
I suppose BackboneFast's main purpose is to quickly establish if the root is still existant in the network or not and re-converge appropriately. And in the case of an increased cost to root, we already know the root is still there since the root bridge information is same and hence it never kicks in.