I skimmed a few seconds of that video and its absolute bullsh!t. Well designed and built transformers have small to negligible external magnetic field so for the coupling between two of them to induce significant voltage in the windings of the second, both must be crappy minimum cost transformers and carefully positioned for good coupling. Also a conventional line frequency transformer will have negligible effective coupling to the transformer or inductors in a SMPSU, as the transformer is designed to operate at line frequency, and the thickness of its laminations are such that eddy current losses will damp any coupling at frequencies above a few KHz, but modern SMPSUs operate at switching frequencies of at a minimum several tens of KHz up to low MHz frequencies. Its about as likely to work as trying to get a steam engine to turn over by farting in its general direction rather than connecting a high volume source of compressed air in place of its steam feed!
If your transformer has a laminated core and you are certain its a mains transformer, measure all the windings on an ohmmeter to find the highest resistance one. That's probably the primary. connect it to low voltage AC (e.g. from a traditional line frequency bell transformer) via a 10W car bulb. You can then measure the voltage on the suspected primary and all the other windings, calculate turns ratios and see if they make sense with that winding as the primary.
If its got a ferrite core or you suspect its an audio transformer, use a signal generator as the excitation source, set to about 1V output, with a resistor in series equal to the signal generator's nominal output impedance to limit the current. start at 1KHz for suspected audio transformers and 100KHz (or the highest frequency less than that your meter is calibrated for, but use a scope if you have one) for SMPSU transformers.