Your primer seating problem is operator error, you don't know what you are doing. Your Lyman priming tool might be out of adjustment, worn components, or you have weak hand strength.
When you "pop" a primer on the Hornady press, you will start a rant about Hornady presses aren't any good. Your problems aren't the end of the world, or a major quality problem at a components manufacturer, but simply you made a mistake and are responsible for what didn't work.
Not all the answers are on YouTube or the internet. There are multiple excellent reloading manuals available. The instructions for your Lyman primer or the Lyman reloading manual would provide insights to your priming problems.
We can't collectively teach you everything about reloading or shooting. Reading and asking questions without condemnation, will solve a lot problems. Making mistakes is also a LEARNING experience, not the end of your tiny universe.
Primers are supposed to be seated below flush. Some cases have tight primer pockets. Some primers may be a tiny bit over size. The population of primers and cases is in the trillions. The largest primer probably won't fit into the smallest primer pocket, and the smallest primer won't stay in the largest primer pocket, but no primer (or very few) stays in an AMERC case when the bullet is seated. That is why collectively, again, reloaders throw away AMERC brass.
Be safe out there. And you still haven't bought us a cup of coffee.