First of all, congratulations on your adoption. I also adopted an adult shelter cat late last year. She was approximately four years old as well.
She immediately went under the bed and stayed there for several days, only coming out to use the bathroom or eat. We just left her alone and gave her time to get used to her surroundings and she was just like a normal cat in not time.
She is now a beautiful, healthy cat who loves attention and is almost inseparable from us. She sleeps on our bed every night, and usually stays in the same room we are in.
Time is the key, and most of us seem to forget that these shelter cats have been thru hell. Imagine how bad their lives may have been before the shelter, and then imagine being shoved into a small metal cage that is surrounded by other scary animals! I think they are in shock when brought to a good home and they are probably wondering if this it's too good to be true!