I wonder if it's more similar to a Soyuz.
The Falcon also stages really early (this allows you to land the first stage), so the 2nd stage MVac engine is more powerful than is really ideal. As fuel burns away, I understand the MVac has to throttle down a lot to keep g-loads under control. I believe it can throttle down to something like 35%. Rocket combustion tends to get less stable at lower throttle settings, so this probably is part of what they're feeling.
The third stage also starts before the second stage is completely depleted; this is why there's an "open grate" visible in photos of the rocket (about half way down the stack, see [1]), gives the exhaust somewhere to go before the previous stage is jettisoned. Hot staging is advantageous as you don't need extra ullage motors to deal with propellant being in the wrong place inside the tanks in microgravity. The Soyuz (and other R-7 variants) are brilliantly engineered; There's a reason they're still flying nearly 70 years on.
[1] https://upload.wikimedia.org/wikipedia/commons/thumb/9/9a/So...
On the other hand you also don't want to turn your crew into pancakes or even make your upper stage look like a squashed can. You have a couple options:
- throttle the engine
- design payload weight, propellant load and trajectory to make g loads bearable till burnout
And one more thing related to stage 2 burnout - precise orbit insertion. Rocket engines used to be pretty imprecise at shutdown, delivering a slightly lower/higher impulse at shutdown at random. Due to this many older rockets have also some small & precise engines to correct the orbit insertion once the main one shuts down - many Chinese rockets have that. As far as I know, the Falcon 9 upper stage engine (Merlin 1D Vacuum) is precise enough so this is not needed.
We'll have to wait for the next mission, which will have an astronaut who has also ridden a Soyuz (and a Shuttle).