Does this word really mean "after"?  Lets take a look:
 

after
3326

 3326 meta {met-ah'}

 a primary preposition (often used adverbially); TDNT - 7:766,1102; prep

 AV - with 345, after 88, among 5, hereafter + 5023 4,
      afterward + 5023 4, against 4, not tr 1, misc 32; 473

 1) with, after, behind

Lets look at other verses that use this very same word.
 

Matthew 26:2 Ye know that after two days is the feast of the passover, and the Son of man is betrayed to be crucified.

Now, is this saying "during" the two days is passover? or is it saying "after" two days is the passover? It's the very same greek word.
 

Matthew 26:32 But after I am risen again, I will go before you into Galilee.

Same greek word again, and the same meaning that it has in Matthew 24.
 

Here are some more examples, all meaning AFTER, and all being this same greek word.
 

Matthew 27:53 And came out of the graves after his resurrection, and went into the holy city, and appeared unto many.
 

Matthew 27:63 Saying, Sir, we remember that that deceiver said, while he was yet alive, After three days I will rise again.

Not DURINGthree days but AFTER.

We can conclude from example that this word indeed means after and not before or during or anything other than after as it is written.






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