Transformers work via magnetic flux. The laminated core of a transformer is composed of ferrous material, which is mechanically affected by magnetic fields. A well made transformer with tight laminations under normal load will resist mechanical movement pretty well, but none do so completely. Yes, all transformers hum, whether you can hear it with the unaided ear or not.
Loose laminations will obviously not resist mechanical movement as well, and can be the cause of noticeable hum. An overloaded circuit, pulling above-spec current, will create a stronger magnetic flux/mechanical effect than the transformer was designed for and likely create a detectable hum where it wouldn't exist normally.
If everything works as designed and you just have a hum, chances are it's a defective transformer.
ALSO....TRANSFORMERS INSTALLED AT THE FACTORY HAVE A VA RATING. MAKE SURE THERE IS NOT MORE LINEAR FEET OF TSTAT WIRE THAN ALLOWED!!!
This is totally bogus with respect to hum. More wire means less load current, and consequently less potential mechanical action in the laminations.