Smoke coming from transformer means........anyone?

The variac method is the very best method for new (weeks or months in the box) and old, although a switching power supply will be toasted by doing this-not a problem with vintage gear.

You failed to mention the make and model.
Is it an older SAE? (Smoke And Explode)

The Varic method should be used with an AMMETER in the line to the DUT (device under test). You monitor the current, and if it starts to swing high, you kill the power...

If the transformer smoked (presumably the power transformer) it is almost certainly toast.

The output transformers are probably worth saving along
with the tubes. Build yourself a nice DIY tube amp! :- )