Okay, before the truce, everything was as it was in the movies. Of course, the redpills didn't know too much before then. We (meaning our redpill characters) were still in the pods then, so we didn't even know there was a Matrix 
The truce is here, and everything is changed. The Merovingian and the machines now have redpills that work for them, because they know that as long as there is a truce there is benefit they can gain from us. The Merovingian knows what happened in the movies, the Oracle knows what happened in the movies, the machines know what happened in the movies, and probably other exiles and programs did too.
Who is to say a redpill or group of redpills didn't sit down with the Merovingian and have everything told to them? Who is to say the machines don't have some kind of report on file for their operatives to look at that has all of the events from the movie in them?
Who is to say the Oracle didn't tell Neo's story to redpills at some point?
There's lots of ways for the information to get to redpills, so it's easy to see how the knowledge of what happened can be passed around naturally 
If you are looking for a reason why your character knows everything that happened, well I guess if you wanted you could say your hovercraft has all the data on file, like a library has history books, or in that time between taking the redpill and jacking in to the tutorial construct thingy, Niobe's crew explained the history to you while you were in the real world.
There's lots of ways you could come up with to explain how your character knows everything 