How does rubidium locking link to PLL?

Yes — rubidium locking and a PLL are closely related ideas, although the atomic-lock servo is not necessarily a conventional electronic PLL in the narrow sense.

Think of it like this:

PLL: Oscillator → compare with reference → find error → correct oscillator → repeat

Rubidium standard: Quartz oscillator → compare with rubidium resonance → find error → correct oscillator → repeat

The crucial difference is what provides the reference. In a normal PLL, the reference might be another electronic oscillator, such as a 10 MHz crystal or GPS-derived signal. In your FE-5650A, the ultimate reference is the atomic transition of rubidium-87.

The rubidium system deliberately probes either side of the atomic resonance. If the oscillator is slightly too high or too low in frequency, the optical/atomic response changes. The electronics turn that difference into an error signal.

That error signal feeds back to the quartz oscillator:

             RUBIDIUM ATOMS
                   |
                   v
10 MHz ---> frequency comparison
oscillator          |
    ^               v
    |          error signal
    |               |
    +---- correction+

As the unit warms up, the oscillator may initially be away from the centre of the rubidium resonance. The control system keeps correcting it:

Too low  → correction upwards
Too high → correction downwards
Correct  → error ≈ zero

When it reaches the atomic resonance and the feedback system can hold it there, the rubidium standard is LOCKED.

So when we say your FE-5650A is “rubidium locked,” we essentially mean:

The control loop has acquired the rubidium atomic resonance and is successfully using it to discipline the quartz oscillator.

This also explains why you get 10 MHz before lock. The quartz oscillator is already running. Lock doesn’t suddenly create the 10 MHz signal; it makes that existing 10 MHz oscillator trace the rubidium atomic reference.

And there’s another level you could add with your Leo Bodnar GPSDO:

Rubidium atoms
      |
      v
 FE-5650A
      |
    10 MHz
      |
      v
long-term comparison/control
      ^
      |
     GPS

That combines two different strengths: rubidium for excellent short/medium-term stability and GPS for long-term traceability to UTC.