On initial reading this doesn't sound to me like a mismatch between the monitor and printer calibration, although there may be some minor misfit there. Allowing for the fact that qualitative statements can be subjective
, having to increase saturation +20 or a description like "images with more 3/4 tone values (RGB aprox 20-60) are not even close" sounds more like something fundamental in the printing pipeline is mis-configured or broken.
If the monitor profile is posted here, some of us could take a look at it and rule out any significant issues with how it's rendering display output. I have to say I'm not a fan of the Spyder products, having tested many previous iterations of them and found them lacking. But I haven't had my hands on a Spyder5 or Spyder5-generated monitor profiles yet. As a side note I also haven't yet looked at any of Epson's canned profiles for the new SureColor printers, but I presume they are competently produced. If this print testing is being done with Epson's luster resin-coated paper, with the associated ICC profile and luster media type selected in the driver, then that should be a pretty bullet proof option in terms of reasonable screen-to-print matching.
So yeah, it seems more likely to me that it's something off kilter in the print pipeline. Wrong printer driver installed on the Mac? Photoshop print settings or Epson print driver settings not fully correct? I don't think double-profiling is possible on Mac OS X any longer; if "Photoshop manages color" is selected then the printer driver colour management is automatically disabled and in fact can't be enabled by mistake.
Photoshop/Mac printing bug? As mentioned by the previous poster, be sure the latest Photoshop CC is installed to correct the printing issue recently triggered by Adobe.