This answer given to this problem was that only one of the double bonds is reduced into an alcohol. I think i understand how the double bond is reduced into an alcohol. An electron is transferred to the carbonyl carbon and the double bond cleaves homolytically, forming a carbanion (stabilised by resonance ) and the oxygen with an extra electron which then will gain another electron and both get hydrogens to form the alcohol.
First of all is my method right? I don't think so as both the double bonds would have been reduced into alcohols. Also i was unable to see any sources for the birch reduction of di-ketones, I was only able to find it for unsaturated ketones.