When cuttings grow from lower buds rather than the ones at the top it means they are too dry. Could have been too dry to start, needed to hydrate first, or maybe the situation is just not a good balance for the cuttings. They can only absorb water through the buried portions of the bark, everything that is exposed will lose water. When rooting directly in cups 2/3 of the cutting should be buried... Because there is already growth burying deeper is not really an option.
What I would do is float the perlite away... If they have roots that look good pot them in a mix, if they have no roots but the bark at the base looks good and does not slip off with gentle rubbing I'd lay them sideways (growths sticking up and out as much as possible) in wet perlite for a couple days to rehydrate, they should make a dull sound when you tap 2 together, then you can wrap the part above the growths with parafilm and pot them in whatever at the same depth. The parafilm ought to prevent the same thing from happening again.
When leaves wilt suddenly though it is usually a sign that the base of the cutting has rotted. That usually happens when there is poor aeration in the center of the containers, either from overwatering, a dense mix, or stagnant air. Rather than just opening the tub up try fanning vigorously with the lid for a minute, this will actually force air into the center of the cups and expose the cuttings to less dry air. If the ends are rotted then it gets harder and more complicated... I trim them back to healthy cambium just below a node. Oh and one more thing to check is the pith at the base, it can be infected and hollow out/turn dark and cut off roots from the top of the plant even though they will still look healthy for some time.
