When will I see this bonus?

Please make sure you read the bonus addendum. They generally state when and how they will be paid. Good luck and congratulations on your extension :-)

What was the end date of your previous contact.
Even if your enlistment date was 16Sept the effective date of the contract won't be until the day after your previous contract.
This is explained in the remarks section.

See if there are stipulations in the contract. Sometimes, a school or qualification is required to pay the bonus.
Another possibility is that the first contract needs to expire before the new one engages. That was a surprise I had on my last contract. I had to wait 8 months for my old ETS before the indefinite enlistment kicked in, and thus my bonus

Finance has no knowledge of these things they only pay them- retention would be your POC. Not sure why they would respond they don't know as this is their job.

According to your DD4, the effective date was 20180917. It generally takes 30 to 60 days to be paid. It was processed thru the G8 on 20181004. You should get it within 30 days.