In Finding Dory, when Marlin meets Dory's parents, it seems as if they all knew each other already. Is that the case? Or are they just recognizing each other based on what Dory had said? I am not sure if I'm missing some previous detail from Finding Nemo.
Yeah you got it right. Each party was able to deduce the identity of the other party based on Dory's brief descriptions and the short bit of conversation they had. The first thing the two parties talked about was Dory so they knew they had that in common. Two Blue Tangs looking for Dory? They're probably her parents, Charlie and Jenny! Two Clownfish, one being a dad and the other his young son, who are also looking for Dory? That must be Marlin and Nemo!