If the Doctor had told her not to touch anything, i doubt Rose would have listened anyway. The Doctor is ever so slighty unhinged at the moment. I don't think he's got all his marbles. Besides he has a soft spot for Rose.
I think he said to Rose about taking Adam along "On your own head be it" or something along those lines. It appears to me at least that the Doctor is teaching Rose about time travel. We don't know how long the Doctor had gone for in the first episode. He could have just shifted the Tardis position or gone back in time and saw that he needs Rose etc. Fanwankery is great sometimes. Must stay out of Doctor Who forums.........