Yes there are going to be different versions of the 'official' story. The truth will come out piecemeal.
First version:
The Sindar and Noldor meet, and the Noldor have to give a reason for being back in Middle Earth. They very much say, hey, we came back to help you fight Morgoth. He's awful, common enemy, let's work together against him. The Sindar might (for the most part) accept this at face value, and some of them even think that the Valar have sent the Noldor to help them fight Morgoth. The Sindar know *nothing* of what has happened in Valinor. Fingolfin probably wants to keep it that way, if he has any hope of maintaining peace between the Sindar and all the branches of the Noldor (including the Fëanoreans) that he has recently become High King of.
Second version: Rumor Mill
Over time, the Sindar learn more of the story - about the Darkening of Valinor, about Morgoth's attack on the Trees and Finwë. About the existence of the Silmarils. Galadriel is the main source of this info reaching Thingol, though by now the Sindar are likely starting to speculate about all the stuff the Noldor are refusing to talk about, and Sauron/Thuringwethil are doing their best to stir up distrust and coming up with their own versions of the stories (bad, but not as bad as the truth). Perhaps they are saying that the Noldor came back to conquer Beleriand and make the Sindar their slaves (or something). Fingolfin would do his best to shut down the rumors, maintain the party line and the strict insistence that no one talk about this. And he would draw on the unrest of the Noldor as his own personal guide as to how *not* to solve this problem. Somewhere in the midst of all of this, Finrod and his siblings have a meeting to discuss their approach to damage control - they are the ones with the most access to Thingol, and are very much the go-betweens. They seemingly agree not to tell.
Finally: The truth comes out.
Thingol's ultimate source of the story is Angrod, who is past done with protecting the Fëanoreans by hiding their crimes. His own mother was killed at Alqualondë, and he has reason to make the distinction between the rebellious Noldor who did not take part...and the Kinslayers. We will need to have some particular incident or event incite Angrod to spill the beans. Certainly, if Thingol has heard enough to know that Olwë was killed at Alqualondë, he could accuse Angrod of being a kinslayer and it could come out that way. But then...how does Thingol find out about Olwë's death? Does he dream about it, or what?