Well, I've been preparing my design jobs for commercial printing for nearly fifteen years. I always press check as color can be bumped in small increments. Press ops don't necessarily see what we see. But a good operator will know how to adjust the color in increments to get what you want.

If you gave them a cmyk file, that's all there should be to it.
Did you give them prints to match from? That's a must.

I think you should ask them the questions you pose here, as they are the ones to deal with. I would leave them to figure it out and not waste your time. When they get a good match, go see it.

Choose a printer you've worked with next time, and one whose quality you are aware of. I've used the same printer for nearly the whole fifteen years for 90% of my jobs because of their QC.

But yeah, ask for a discount.