To parallel three-phase ac generators, three things must be identical: phase sequence; voltage; and frequency.
Phase sequence must be the same, abcabca... In the video, all lights are dark or bright together. If the phase sequence was incorrect, one would be bright, one dark and one dim.
Voltage is a little tricky for induction motors used as generators. Synchronous machines allow adjustment of excitation to adjust the voltage produced. The voltage you get with induction motors is not adjustable.
Generators are driven by prime movers. A diesel engine, steam turbine, water turbine (water dam). The prime mover determines the frequency.
The video shows synchronizing induction motor generators using sychronizing lamps. Normally (on ships), you would have a synchroscope with synchronizing lamps as backup. Actually, if you were just doing it with lamps, you want to have frequency meters. You want the oncoming generator to be running a little faster than generator on the bus. You close breaker at 11:55 or as lights go dark. In the video, the second time he does it, he misses it slightly.
You want it dark because that means the voltages on either side of the lamps are the same. If they are not, the online generator(s) force the oncoming generator to be identical to bus. The will be driven as a motor to be in step with bus. The brighter the lights when the breaker is switched on and the more current that will flow, possibly tripping breakers.
You want the oncoming generator to be running a little fast as it comes online, so that it will take up it's share of the real load, the kW, from the prime mover. Excitation of the generator will control the reactive power balance, the kVAR.
If you have multiple generators online driving a load, the action of the generators will keep themselves balanced.
If one generator slow downs, it delivers less power to the load and starts to speed up, then the other will deliver more power to the load and start to slow down. This continues until both are producing the same voltage, power factor and frequency.
If there is a difference in voltage between the generators, current will flow between the generators. The generator delivering more of the load drives the other as a motor forcing it to stay sychronized.
Think of it like two clydesdale horses yoked together pulling a load. They both have to go at the same speed to move the load.