Mixing the fixed-price and hourly contact models together like this USUALLY ends in disaster.
Maybe you are the exception. I don't know.
I can not imagine any competent project manager who would let you do something like this, though. They would tell you that this sort of stunt will almost certainly derail the project timeline and blow up the budget.
At this point my advice to you is to monitor the project deliverables closely and stay in frequent contact with us in the Forum, where we can offer some objective advice.
If you have a fixed price why didn't you set it up as fixed price? There is nothing to stop the freelancer continuing to bill hours after $1,600, and if they do then Upwork can't help you. If you have a fixed price it's far safer to set up the contract as a fixed price contract.
The flip side of the coin is this:
After the freelancer bills $1,600, if he then stops logging time...
Then it would seem that the freelancer would have little reason to do any more work on the project.