Nuclear umbrella is a collective nuclear security agreement between a nuclear power state and other non-nuclear states in which the former provides a nuclear security to the later as we have US providing nuclear umbrella to Japan.
Over a period of time since the cold war, the umbrella states have changed their strategy towards disarmament campaign considering the new emerging geo-political and diplomatic situations. As of date umbrella states are divided into two groups. One state acts as a proxy for other nuclear states to scuttle such disarmament campaigns while the otherd are in a fix as to what action can be taken.
During the recent open ended working group meeting, umbrella countries like Australia who earlier supported CTBT , voted against the resolution to bring a legally binding agreement for nuclear disarmament in 2017. Other umbrella countries like Japan, however abstained from the voting.
It is obvious that all the umbrella countries are taking decision based on their economic, political and social, security and diplomatic concerns, however for the welfare of the whole humanity, states whether nuclear or umbrella start looking beyond their political boundaries.