You can check the reimbursements by going to the Fulfillment report page and clicking reimbursements.
You'll need to check back regularly, once a week at least, with the oversized inventory and open cases whenever you see things that look like they shouldn’t be oversized.

You can only cubiscan each product once every 30 days so I suggest keeping track of every case you've opened in the last month that way you can see if it's been cubiscanned recently. If it has been cubiscanned in the last month and is showing up as oversized again, you can open a case and ask them to correct it based on the information from the previous case. They won't remeasure it but if you ask them to reference the old case id they'll usually correct the dimensions for you.

Use this case template:

"Please reference case id 12345678653 and correct the dimensions for the product (ASIN).  It was recently cubiscanned and the dimensions were corrected but now it's showing up as oversize again.

Thanks,
"Your Name"