There are a couple of important "IFs" here.
IF the tank had an active biological filter going during the hypo treatment, then you're 'ahead of the time' by having an established and functional biological filter intact. In other words, your system doesn't have to wait for the build up of its biological filter. you've cut this time off.
But, IF during the hypo treatment you found spikes of ammonia and nitrites, then your bio-filter wasn't either able to keep up or was partially working or the worse case scenario: not functioning at all. In this case some time has to be set aside for the bio-filter to recharge itself. This is the scenario that would mean your tank would go through another cycle.
I don't know which of the above two possibles apply in your case, unless you've been collecting test data then and now on the status of the biological filter.
My concern now is the 'month.' Are you sure your display tank is free of Marine Ich? The reason why I am concerned by this is that the usual hyposalinity treatment is to run hyposalinity until no more spots are seen on the fish. Then you continue the hypo treatment for another 4 weeks. If any spots show up, you start the clock again. You have to go a full month without seeing spots. Then, you raise the salinity back up (that takes a week) and observe your fish for another 4 weeks to verify that the treatment was a success.
The minimum treatment time is at least one month, with the usual being about 6 weeks. The whole process takes longer: Then with 1 week of raising the salinity and the 4 additional weeks of observation, you're talking about 10 weeks minimum for the process. Don't assume anything until you've let the proper time go by.
The Atlantic Blue Tang, a.k.a. the Atlantic Yellow Tang (because as a juvenile it is yellow) is a fish that likes a lot of swimming room. The min size of its final tank should be no less than 100 gallons. For a few of them, you want at least a 180 gallon tank. Since the size you've indicated is that of a juvenile, and if you put them in the QT at the exact same time, then the 40g should be okay just for the quarantine time. Provide plenty of plastic hiding places (pipe and/or decorations). For your QT to be able to handle this bio-load, it has to have an operating bio-filter or you have to be prepared to do daily water changes, and/or you will need some chemical filtration support.
It sounds like you understand the advantage there is by taking things slowly! :rollface: