I believe you misunderstood the intention of my post. What I wanted to say is that whatever we do (or rather what
@QuietMaple adds to the designer), we will never be able to get a color representation that is accurate enough for advanced designs with color matched inlays. This would require support from Tina, and it looks like they are not running a process to provide that support.
I find the abscence of proper color management nevertheless surprising, and the low price is not an excuse for that. For comparison: You can find cheap book printing services in China who will deliver whole books - printed, bound and shipped - with an acceptable level of color management. As far as one can tell from
@GreatWhiteDope 's photo, the external label printing service did a pretty good job, too. The label colors seem to be very close to the design.
Would I still consider Tina's for a custom set? Well, yes. It is probably the best option in the price range. I would adjust my expectations accordingly, and I would not attempt to do color matched labels, especially not faux shaped labels.