Indeed, English is not my first or only language. But still, You seem to get the core of the message.
When passengers start to wander the cabin during taxi, it is easily noticed in the flight deck from the cabin crews PA orders to sit down again. Having the PA volume control on the audio selector slightly open helps quickly notice developments in the cabin. Passengers appear not to understand those cabin crew-given orders too well though, they often see no reason to obey as they should. A smooth stop (certainly not by slamming the brakes, you do not want to injure anybody!), if considered appropriate a word to the ground controller, and most importantly an announcement to the passengers from the flight deck has much more effect here.
First of all, the passengers, all of them, notice the stop. When the flight deck then places the blame for this on the easily identifyable group that has stood up against regulations and orders, there will be peer pressure among passengers. A lot. All of them want to get off the aircraft, many will have connections they hope to reach, it may well be that the flight is delayed and those connections are quite critical already. The other passengers fear of missing the onward flight is therefore focussed on the standing passengers within a second. The critical ingredient here is the stop, which can only be delivered from the flight deck.
The reasoning behind this is clear: the cabin is no longer secured and, should there be a reason for an emergency braking due to a vehicle crossing in front or something else that has often happened on a crowded apron, there is no longer time for an elegant stop and there will be injuries. The stop is therefore clearly for safety reasons and a most prudent course of action.
In my experience, such a stop never takes longer than 30 seconds. When the cabin crew then confirms that the cabin is secured again, there is no reason not to continue to the gate. During deboarding, the premature wanderers are usually rather deflated (although a little miffed maybe) and there is no need for further explanations.