One thing in engineering is the first one is the hardest to build, the others get simpler each time since all the bugs are worked out (Geonosians? ).
Is this reference to the second Death Star? I thought I read somewhere that it had been under construction a long time before ANH as a back-up to the original, but the wookieepedia does say it was built after the destruction of the first one.
I would think, in my opinion and not going on material, that they worked on the second in tandem or shortly after completion of the first since I find it hard to believe that in 3 years they had one mostly completed (not sure the percentage). If the first one took approximately 18 years to build, I find it hard to believe the Empire could build the second just as fast... maybe 15 years, but not 5, like you might guess with how the incomplete second one looked in Jedi.
I think the second was built in a completely separate location, secret even to the personnel of the first, so if one was compromised by spies, then the Empire would still have others ready to go.