MSP controller described a potential conflict event when coordination by the supervisor following a runway closure; was confused; the reporter indicating the coordination should have been confined to position controllers and accomplished on the land line.

Narrative

A bird strike occurred on Runway 30R which closed the North Runway. I coordinated with Local Control North that I would own all departure headings working Runway 30L; Local Control South. I also had all arrivals now for Runway 30L and Runway 35; Local Control West combined. I had all departures; including the north bounds due to the runway being closed. When Runway 30R opened again; my Supervisor advised me Runway 30R departures resumed; and he got priority. I responded 'he has his headings back' then I moved my northbound departures out of the way because I didn't own north headings anymore; so I could get my southbound departures airborne. Local Control North departed a southbound CRJ with no coordination; I was crossing Runway 30L with Runway 35 arrivals; I had an arrival and I had a southbound in position; Runway 30L. I departed 30L; turned and shipped Air Carrier X. When I looked at the D-Brite for my next arrivals; I noticed the CRJ airborne in front of my MD90. I didn't believe I had 3 miles; I alerted my Supervisor of this; plus the fact that there was never any coordination to use my airspace. My Supervisor took me off position and explained to me when he/she coordinated with me that Local Control North had priority it meant Local Control North owned all headings. I said I only returned Local Control North's headings. We looked at the replay of the incident; it was determined separation was never lost. The Supervisor should have had us Local Controllers do our own coordinating and it should have occurred on the land line.