ksner,
In my experience it is not unusual for harmonics to show up in cases of severe unbalance.
The unbalance was likely inducing enough energy into the fan? to exagerate any looseness in the machine ie. bearings, base, duct work, piping, motor covers, gaurds etc.
The 3X vibration is probably the location of a resonant frequency, and after balancing the forcing frequency disapeared and thus the 3X.