I haven't actually used offline tiles myself, but based on this thread it looks like you might need to put the RMDBMapSource into an instance of RMMapContents instead of directly into the MapView. So I'm thinking it would be something like this with Xamarin:
RMDBMapSource dbSource = new RMDBMapSource ("Philadelphia.mbtiles");
MapView = new RMMapView(View.Frame, new IntPtr());
RMMapContents contents = new RMMapContents (MapView.Handle, dbSource.Handle);
That assumes you have a wrapper binding for RMMapContents too which from the looks of it the bindings project does not have by default. You'd need to throw in a wrapper that at least defines the constructor.
This page looks like it provides similar code (in Obj-C) towards the bottom.