This is perhaps the most classic example of an incorrectly configured color management system that I have ever seen. I first experienced this same issue in the late 90s, and seen it repeatedly over the past 15 years or so. Within the visible spectrum, blue is directly adjacent to violet (and indigo), toward the lower frequency end.
As such, it doesn't take much being wrong somewhere for blues to print purple, or vice versa. Moreover, unless your display is properly (and recently) calibrated, there are no guarantees that the blue you see on screen is really the color in the file to begin with. In other words, the problems can and often do come from various places, and to truly solve this problem, as opposed to the various band-aid fixes that many will recommend, involves an investment in instrumentation as well as investments in time to learn what is really happening. You cannot fix a problem until you understand all of the variables involved.
If this sounds like a lot of work, you're right. There is a lot going on behind the scenes, that most users (even a lot of experienced ones) are completely unaware of. Only around 1 PSP in 20 properly and consistently runs a custom end-to-end color managed workflow. It's not easy to implement one in a commercial sign shop environment. Due to the tremendous variety of media, we have many more problems to deal with than a typical offset printer.
Here are a couple of resources that you might (or not) choose to review:
Color Management Professional Certification:
http://www.idealliance.org/products/color-management-professional-fundamentals-20
Click on the 'View Sample Lesson' button to see the first training module of this program (it's free to view this lesson)
ICC Web Site (International Color Consortium:
http://www.color.org/
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