Synopses don't actually have to tell all the events in the same order as the novel, but most of them should be, & I think the important ones definitely should be. For example, if it's not important enough to mention a scene where the MC meets a new character but that character is important later, it's perfectly fine to say something like, "MC visits Side Character 13, who he met earlier...." But if you're revealing that the MC's Uncle Bob is the killer he's been searching for, you don't want to start out with, "MC begins his own amateur sleuthing, never suspecting that his uncle is the one behind the deaths."
In this case, I'd say definitely show the twist as something the MC finds out later. The point of the synopsis is to demonstrate to the agent/editor that you can write a novel with a beginning, middle, & end, & to give them a general feel for what the novel contains (whereas a hook in a query, is just to show them that you have an interesting idea & maybe they'd like to know more). Showing that you can add a twist successfully is much better than telling the agent what's up right out of the gate. It gives them a better feel for how the novel's going to read, & allows you to insert the MC's shock into the synopsis better than if you had told the agent upfront about the twist.