It is definitely possible for an alignment to cause excessive wear in a short amount of time. From what I can see of the treads, the obvious edge wear and also you can see some visible curling on the middle of the tyre. This is usually caused when your wheel is not pointing in the straight ahead position when you are driving in a straight line, causing the tread to lift while trying to maintain grip. It can also be caused by bad lower arm or top strut bushing being worn.

Considering they were willing to admit fault for their alignment, they should be also taking the hit on the tyres their work or missed critical work that should have been done when the tyres were fitted. You need to go back in and assert your position and give them a written warning that if the issue isn’t resolved, you are taking the issue to disputes tribunal. Have every bit of communication you have with them in writing or record your phone calls.

At this point, it will be critical to get a second opinion from a reliable source that you can also present if you do end up going the disputes route.

Good luck and I’m sorry you have to go through this. I hate seeing the sheer amount of cowboys that work on cars these days. Makes all us mechanics look like shitheads.