As you know, there is something called Uk. That is the voltage drop from idling to fully loaded secondary. The reason is the stray inductance that is present in the transformer.
To be able to deliver rated voltage at rated load, the transformer is wound to compensate for this voltage drop. I.e. the secondary has more turns than the simplified transformer formula says. If the Uk is 10 percent, then you will have ten percent more turns.
Now, if you run this transformer backwards, you will not have nominal voltage even when idling. You will have about ten percent less (because of the turns ratio). Further - if you apply rated load to the "secondary" (former primary) your voltage will drop another ten percent. It is not unusual to have a "loaded assymmetry" about 20 percent in small transformers. It has not much to do with undersized windings - it is just a fact of life.
You can probably get a transformer with very good regulation, say 1 or 2 percent, but it will cost and you will still have that voltage drop (2 - 4 percent) if you run it backwards. Trust your manufacturer - all are not crooks.