Temperature in the environment
This would answer both cases.
Balloon shrinking: causing the papier mache to wrinkle as the form it was set on changed.
Balloon expanding: causing the papier mache to expand and crack while setting as the balloon is getting larger.
It is important for the project to dry in the same environment (temperature) in which is was created. This might seem obvious but small changes can affect this. Time of day for instance.
Expansion and Contraction
If working indoors the sun might not be directly on the project initially. If left for many hours after, layers may dried with heat from direct sunlight that could make the balloon inside expand.
The opposite could apply as well. If the project was in direct sunlight while the layer was being applied it could have then cooled while it was still setting. When the base you are forming your project on moved it will set in unexpected ways (turning into a raisin).
The balloon shrinking is less of an issue after several layers. Having 2-3 already dried layers gives a good base so the balloon shrinking would be a non-issue.
This also could happen if you take the balloon outside for example to have it set faster. A change in the environment while the balloon is drying is likely causing this to fail.
Keep the project in the same place and avoid changes in temperature. This is more crucial for the first few layers.
A wrinkled balloon can usually be ignored by adding more layers, assuming the project calls for it. As layers get added the imperfections are hidden.
A busted seam (or join) can also be fixed by patching with more papier maché. In the case of the piñata, this might be less than ideal, as it introduces a weak point. Setting layers with the paper strips perpendicular to each other can help fix that.