I remodeled my kitchen almost 2 years ago. I had buddy help me install all the cabinets - base and wall. I told my wife that I would have the countertop professionally installed just in case of a screw up.
First they ordered the wrong edge on the countertop for another customer with the same design and color we wanted. They offered a discount if we would accept it and we did. They messed up the 45 degree cut in the countertop and had to take it out and re-install it. I also felt like the sink cut out was too big for the sink we installed. This company came and took measurements for the countertop and I even had the sink there for them to measure for the cut out. Then 2 weeks later, we noticed a 3" crack in the countertop. We called the company out to look at the crack. They decided to replace the whole countertop with the correct edge at no cost to us.
They removed and re-installed the sink and all the connections including sealing the sink edges. They did not do any damage to the cabinets. I was really impressed with the work they did the 3rd time. The first installers were not as experienced as the last ones. The company admitted that to my wife when they installed the new countertop.
I would say that no counter installers are 100%. I am sure almost everyone of them have had to install a countertop a couple of times to get it perfect. My $.01 is to let them fix the problems. Be upfront with them in what you expect for them to fix if they mess up the wall.