Do we get the daily incidental reimbursement during AT when quarters and meals are provided?

No.
Incidental Expenses, the IE of M&IE is authorized when you are traveling TDY on an approved travel order (DD 1610) in DTS.
A unit's annual training is typically not TDY travel.

You're only going to get paid what is designated in the orders that will be issued for your AT.

When I go to AT in the field it's CUT AND DRY. I don't get anything but the regular pay to be there, we go there via military vehicle travel (convoy) stay in the field (no housing) and eat in the field (directly from field kitchens). So there is nothing extra coming my way.

Now, when I got to Korea for example, we fly commercial, and eat in the DFAC, and are house on post. So:
1) Housing is a non issue since it's on post there is no money flowing back and forth.
2) Commercial air is via DTS, and all the orders and documentation have to be uploaded and processed once back from the AT so the flight is paid against your GTC.
3) Meals is basically like a scam. We get additional meals funding on our orders, but since we were given DFAC accessibility those funds are taken back as a deduction.

Additionally........... at my higher chain of command levels (I think it's the 2-Star) any additional payments we might get in our orders that isn't directly salary or BAH related go against our GTC. So any extra money we might be getting gets tied up against our Citi card account for a few months until everything settles and then Citi finally tells you that you have a credit that you need to personally request so you can FINALLY get those funds.