What a mess.
Whoever put asphalt or metal on a flat roofing area, even anything below 3/12, is a f++++n' idiot.
It will always leak and be a mess.
Find someone locally who does IB Roofing http://www.ibroof.com/. Get them to strip off that metal and asphalt and tie in properly onto the sloped roof. IB is a permanent solution to this if you don't wish any more problems.
Otherwise, get up there with a case of Lexel after each rainfall and start gooping..........
I'm on "The List" and I love it!!
I am not sure what tinmack want to say, but you can easily fix this problem. What you do, take some flat thin fiber roof strips around 3" wide. Put those in the inclined position over the seam, use white cement to fix it from the outer side where it touches the metal roof, and from other side where it touches patio room roof. I hope this might work.