I have not been able to take that train yet, (it was cancelled when I was booked on it, September,) but I think they do it that same way, allow Brussels and Lille passengers in one part of the train and UK passengers in the other part.
The platform in Amsterdam has a barrier, so they can keep one part of the train in a restricted zone, while the rest is open to 'all' passengers. I think they build it like that in Rotterdam as well.
In Brussels you clear the part of the train the Brussels passengers used and do not open the doors of the cars the Amsterdam and Rotterdam passengers use.
You can then allow new passengers in at Brussels, repeat in Lille if needed and you can now go through the tunnel.
I was going to post this as a comment but it became too much an answer, so posted as an answer even though I have not seen it happen.
Early 2024 version:
There is a gate across the platform they can and do close between the last passengers are allowed to check in and the arrival of the train. One of the staff will be on the platform near the track to prevent people to get around the gate.
Late 2024 version:
Because of work in the station in Amsterdam platform 15 is closed for a longer time so no UK Eurostar train passengers leave from Amsterdam directly. If Eurostar trains to London leave from Amsterdam all passengers will have to leave in Brussels. I have not found any London to Amsterdam trains so I assume that there are no direct trains at this time.