partly correct.
The first aircraft, F-WWOW (MSN 001), has been seen in SIA and QF livery and is the first flying A380' (there are two others for structural tests). The first serial model for SQ will be MSN 003, F-WWSA.
The one in EK livery is F-WWDD, MSN 004. It is the second aircraft. Both will remain longer in service as a test aircraft.
EK and SQ have signed the contract with AI at the same time, but SQ a little earlier, so both can say they are the first to fly the A380. SQ will be the first to put it into service.
I might have to tell you that it's even more complicated: The production sequence is also not in order: first they complete MSN 001, then 004, then 002, 007, 003, 005 and 006.