I am not presuming as to when they had sex or where only that at some point after the birth of Jesus that had a "union".
But that's not what the Scripture says, if you want to read it in your way. It says they had no relations until Jesus was born. That means right then and right there.
Would a natural English speaker say "I didn't get up till noon" if he in fact woke up at 2PM?
Would someone say "I studied mathematics until I was 18" if he in fact studied math all through college?
Would someone say "I never believed in love at first sight until Susie walked into the room" if he fell in love with Kim?
No. The word, in your interpreted usage means that one state of affairs is true in the first half of the sentence and a different state of affairs is true in the second half. And the moment identified by the "till" is the moment of change.
Can you give one example of the word "till" being used in this manner, to mean "everything I just said changed, but not at the moment I describe, but at some indeterminate point in the future."
I'm sure the folks at Oxford would be interested in this new meaning of the word.
SD