Yup, as stated above, the proper first step is to calibrate your monitor. Better calibration hardware/software will also give you a report specifying the accuracy achieved by the calibration/profiling process. I mention this because some monitors can be run through the calibration process and still look awful. Many laptop screens, particularly, older ones, had this problem.
The second point in the workflow where purple-blue errors like this tend to arise is because there are a zillion variants of CMYK, one for each combination of inkset, paper, press / printer settings, etc.
To head off exactly this problem, pro level printers will always supply you with a ICM profile for their particular process. If he did send you one, Google how to install it in PS, turn on "soft proofing", and see how it looks (on a calibrated monitor).
If this printer didn't supply one and doesn't even know what and ICM profile is, and/or doesn't know which variant of CMYK to tell you to use, then either find a better printer, or send him the file in sRGB. Low end printers (eg, print shops catering to local businesses, eg., Staples, Office Depot, etc. in the USA) usually muck up sRGB much less than CMYK.
Finally, if you don't want to do any of the above, send the file to me and I'll tell you how it looks on a well calibrated NEC Multisync monitor designed specifically for color critical work.
If you don't even want to do that, use the Photoshop eyedropper (Google {photoshop eyedropper readout}) to measure the average hue in some representative patch of purple color. Get hold of an on-line color wheel, and see how the hue you just measured (in degrees) compares to the range of hues occupied by purple.
HTH,
Tom M
