Jason said that the new semester starts on May 7, .....?
1) didn't he
2) doesn't it
Which one? I would choose #1
To expand 'didn't', you would get: anonymous Jason said [past] that the new semester starts on May 7, did he not? He did. [past] So yes, you're correct.
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To expand 'didn't', you would get:
anonymousJason said [past] that the new semester starts on May 7, did he not?
He did. [past]
So yes, you're correct.
The semester, though, does start on May 7th.