Both yes and no.
AIM-120B are from the 90's, deliveries began in 1994.
AIM-120C came in 1996, but they have been upgraded multiple times. AIM-120C-7 was tested in 2003 and I believe is the one that is being exported.
Which one DCS models I don't know.
But there is a big difference in between the different models.
There's also the AIM-120D, that came in 2008, but is not yet modeled in DCS World.
Small edit:
I see Frostie posted that it's the AIM-120C-5. If that's the case, that one came in 2000, so no longer 90's missile.