It is an interesting demonstration he puts on.
It is not unreasonable to assume that the Yellow flame color is due to the Sodium ions present in the water. The Sodium [Chloride] does not really have to react itself to give impart the yellow color to the flame; you could just stick some salt into an ordinary flame (example, a non-luminous butane lighter’s flame) and turn the flame yellow, then you could pull out the colorant and it should still be NaCl and the flame color will return to normal.
The yellow color Sodium ions impart in flames will easily over power other colors due to other salts present.
Could it be that he is, very, locally heating the water up to a temperature so high that the decomposition reaction becomes spontaneous (2 H2O --> 2 H2 + O2) and then the H2 and O2 bubbles float away and get burnt. In the process of bubbling up, small droplets of NaCl solution get thrown up into the air and the water soon evaporates leaving small NaCl particles in the flame which act to give it the distinctive yellow color.
But if water is really decomposing and both H2 and O2 are produced, the I would have expected the combusting gasses on top of the test tube to behave much more explosively. If you ignite a mixture of H2 and O2 gas in the proper proportion, it explodes quite quickly with a load pop, it does not burn slowly like a candle wick,