ZKX Controller described a 'spill out' event that resulted in a conflict with IFR traffic conducting weather deviations.

Narrative

Fighter jet Y was operating in the Coastal 1E; 1W; and 2 MOAs and was in communication with Townsend Range Control. I observed fighter jet Y spill out of the MOA on the south side. I contacted Townsend Range to alert them that I observed the spill out. I informed Townsend that I would be having traffic passing on the south side of the MOA and I could no longer allow spill outs. The traffic I was controlling was also trying to stay north of thunderstorms. Air Carrier Z was descending to 11;000 FT; eastbound; passing to the south of the MOA and Air Carrier X was climbing to 10;000 FT; westbound. I informed Air Carrier Z of the spill out and possible traffic situation. Fighter jet Y appeared to be maneuvering northbound away from traffic. I called traffic between Air Carrier Z and Air Carrier X. I then handed off Air Carrier X to sectors 29/79 and gave this aircraft the frequency change. I observed fighter jet Y spilling out of the MOA once again; causing the conflict alert to be set off. I was not in communication with either aircraft. I would suggest that military operations understand the importance of staying within designated airspace and easier communications with the Range Control in communication with the military aircraft.