Astroturfing is actually appropriate. The movement pretends to be grassroots. This looks like it was organized in multiple states (possibly even countries) by the same organization, that's not grassroots.
It's kind of a grey area and debatable. A group of people starts protesting on a small scale, and then quickly gets a lot of professional and political help, along with a lot of attention from media that wants to push a narrative.
My point was that, for something that is fairly grey such as the coordination versus spontaneity of protesters, you're not going to get solid evidence.
Any disinterested search for truth here would involve reams of original-source facts. This is probably not the right forum for that.
FWIW I did not make the claim for which you are requesting evidence. I just don't think asking for evidence in this case will be very fruitful.
You are right. I suppose I am too loose with my understanding of action as a byproduct of external influence versus direct sponsorship. As an example, the former would be a vague cultural sublimation of influence from a position of power, and the latter would be an immediate demand from a position of power.