Dreams Can Come True

Please be gentle on a newbie...

I don't want to buy the MIAM theory, but I was asked a question today that I could not dis-prove:

How can Neo see Trinity's death so picture perfectly if it is in a dream he's having whilst sleeping in the real world ?

Please help me shut him up !!!

More importantly, how did The Oracle know that he's having these prescient dreams? She knew that he foresaw Trinity's death, and also saw himself walking into The Source (through a door of white light). Neo sleeping in Zion is not supposed to be plugged into anything. Is The Oracle merely guessing that he's having these dreams, or able to see them in his head from memory, or able to see them in his head as they are being dreamt up, or is she feeding him these dream visions?

Okay, so that was too many choices for an "or" question, but then again I'm no programmer.

..or to expand, if he is sleeping in the real world, how can he have dejavu of things that happen in the Matrix ?