There was a belief that activating de-icing boots too early could result in an ice bridge forming over the boot and rendering it ineffective. This led to a recommendation that de-icing boots should not be activated until a significant build-up of ice had occurred.
Recent testing has established that modern de-icing boots are not susceptible to this problem, and advice from the FAA has been changed.
In InFO9007 (dated 5th May 2009) the specific advice given is:
Pilots should follow the boot activation and operating procedures
specified in the AFM or FAA approved operator’s manual for the
airplane they are flying
If the AFM does not have specific boot operation procedures or if ice
thickness is difficult to judge, pilots should not be reluctant to
cycle modern boots at the first sign of ice accretion and then as
A 'modern boot' is defined in the same publication as having
less than 1.75 inch diameter tubes, operating pressures of 15 psig or
greater, and fast inflation/deflation times
It also suggest that any aircraft built later than 1960 is likely to have modern boots.
Essentially, for most cases that you might encounter the video clip is correct, and your class instructor is wrong.
That said, the definitive guide should always be the Pilot's Operating Handbook for the aircraft you are flying.