He was there during the Mount Massive incident to escape the chaos, not for 4 years.
Like in every mad scientist story, it's easier for them to operate under the guise of death, rather than being considered alive. In relation to our world, real Nazis that were redistributed throughout western countries were never registered under their own names and were labeled as deceased, making it easier for them to continue with their experiments, the same way Rudolf did.
the death certificate dates back to 2009, the main events in 2013. the thing i can't make sense of is that apparently the staff working there wasn't aware that dr wernicke was still alive and yet Billy knew him and was still in communication with him for all those years.
it's a fragment of information that i think was either poorly exploited or simply not explained in a way that was functional to the plot.
but i mean, this whole game is overall full of holes for doubts to grow rampant, so im just rambling
If you're referring to the location where you meet Wernicke, then I'd say he simply sat there and waited for Murkoff to intervene in the current situation. The date itself just indicates when the death certificate was printed. It's a mystery as to who they were trying to deceive with it. And yes, there are a number of plot holes that were never fully addressed. There's a document that's listed 4 days after the current events, which might have been a mistake on the developers' part. Red Barrels never went into fully explaining the overarching story, but preferred to leave it ambiguous.