i've just checked the Omega site set up by the late Chuck Maddox, the reknowned world expert in Speedmasters, and what he states in one small section is that your caseback is the second generation of 'flight qualified' casebacks with the added 'first watch worn on the moon'. when this caseback was first used is not clear, but the first gen came was introduced in late 1969 and ran until 'possibly' 1971-1972.
the only way to clear this up is to ask for a pic of the inside of the caseback as most, not all, but most of the ref numbers have a date as well ie ST 145.022-71 or 145.022-71 ST. if it has the date code then you will know if it matches the date given by the seller.
i cant see the movement number clearly, but for it to date from 1970 it needs to be 28mil-30mil. it looks to be a higher number than that so it is later..
its entirely possible that the movement date and caseback tie up nicely, but the seller has got the year wrong. thats very common as a lot of sellers dont really know the correct dating.
i hope i havent confused you with too much detail, but these details can make all the difference.
best
Graham