I referenced that video (or another in the series) in my answer to Electrical phase in a power grid and power transmission which may help.
In the video below, somebody synchronizes two 3-phase generators ...
In electrical engineering we often refer to these as "machines" rather than specifically as a motor or a generator because they can operate as either. If connected to the grid and driven they will act as a generator and export power to the grid. If a mechanical load or brake is applied to the shaft they will act as motors and import energy from the grid to drive the load.
Figure 1. A generator and load on three-phase system. Note here how both machines are in synchronisation due to their direct connections. Image source: Instrumentation Tools.
Why does this autosynk happen?
I've explained how synchronisation is achieved in my other answer and you've summed it up at the top of your question. A better follow up question might be, "What would it take to break synchronisation?" The answer is that you would need to exceed the machine's capability to stay in synchronisation.
- In the case of the motor you just have to apply a large enough load or stall the motor. The problem is that the motor will draw more current to the point that the windings will reach extreme temperatures, the insulation burn off and internal short-circuits occur followed by smoke and fire. To prevent this overload trips are installed which allow short overloads during startup but trip out on a prolonged fault to protect the motor.
- In the case of the generator being over-driven a similar situation will occur when the generator tries to export enough energy to speed up the whole grid. Again, an overload will trip out to protect the machine from overload.
Have a look at my other answer and see if the combination answers your question.