Sounds to me like the circuit feeding the barn was existing. Minimal wire was used to feed the barn.
The OP asked the electrician to check the system. he found that the line loss was excessive and suggested installing a bucking transformer.
Everything the OP's electrician suggested is correct. Problem lies though in the system check. He should have verified the output voltage both under load and without any load. Not a big issue if the transformer he used has input and output taps. Output taps maybe enough to adjust voltages.