I can still remember a time when every primer and every case was precious due to my very limited budget, and that was back when we had $.20 hamburgers and $.40 gasoline...primers were less than a penny then, but still quite dear.
Today, I would toss a flipped primer without hesitation. Steady pressure on the anvil (like from seating it) CAN fracture the priming pellet and lead to less than correct ignition or even total failure. It doesn't always do it, but it can.
Bottom line, seating a upside down primer is YOUR FAULT. YOU failed as QC.
I have done it a couple times in 40 years of loading, every time with a press mounted system on a single stage press, or on a Dillion progressive. If the primer bounces in the cup, and you don't notice it, can be upside down or sideways, and its your fault.
Be honest and admit the mistake, and increase your inspection diligence. If your loading system doesn't let you see every primer right before you seat it, get something that does!! Forget speed, do it right. In the long run, its better than doing it faster with more mistakes.
PUSH the primer out DO NOT TAP! then either reseat it and pop it off in a gun, or toss it. Don't let it get mixed in the "good stuff". Also wear safety glasses and gloves, just in case!