Well, you've stumped me then, because I haven't heard of any Costco minilab that can do an on the fly conversion on a tagged AdobeRGB file to an internal printer profile loaded in their software.
As far as I know, the DryCreekPhoto database profile I use with my Noritsu was created from the regular dumbed down push button settings they use with all their customers so nothing has to be specially chosen within their software. The only thing operators LIKE to do is fiddle with color and density bias with very limited editing tools and they need to be told NOT to do this.
These minilabs if calibrated and maintained on a regular basis will usually print a grayramp that looks pretty close to what is seen on the monitor, meaning it prints in a linearized stable and constant state as long as you use the same settings everytime from which the profile was built from.
I ask the operator if they change any software settings specific to my files and they always say they run my prints using the same settings they use for everyone else including my sRGB target print I use to test for printer drift. They indicate they don't have time to change any settings because they weren't trained to know anything else about the printer software's standardized settings. And when you see the volumn of prints they need to generate you can understand why.
I just know they are off, not you. They need to fix it on their end. Don't take no for an answer or you'll be on a troubleshooting excursion that'll waste your time like you'ld never believe. Find someone more knowledgeable than the person you're dealing with if you don't get the answers you need. I know for sure you shouldn't be having this much trouble with such a stable well behaved printer like these minilabs.
I wish I could help you more.