Yes. You provide both a CMYK and Pantone color build of a logo, as well as an RGB/Hex build, to the client. Whether a client asks for it or not a professional's job should be to provide everything the client needs, even if the client is unaware they need it.
When I start adjusting the color of a logo I am designing I use Pantone colors. The reason being that, in practice, a Pantone color is always going to be that color when reproduced professionally. So, I want to design with the most common denominator.
After I settle on coloring, I look at conversions. I never trust any software to convert the colors for me.
Software can be pretty accurate most of the time. But there are cases when it isn't. Software can be wildly inaccurate in some cases. I mean wildly. I've seen a yellow become a green when allowing software to automatically pick a closest CMYK color referencing a Pantone color.
So I start with something like Pantone 248... allow software to convert it to CMYK.. then adjust the CMYK values to better suit my personal preference.
In this case I see the software conversion wants to use 2% of black. But no commercial press is going to hold a 2% screen very well. At a minimum a 2% screen is going to be difficult to maintain. So, I personally adjust to remove that 2% black screen, adding a touch more cyan to compensate.
I then allow software to automatically convert my CMYK choice to an RGB choice. CMYK to RGB conversion is generally more accurate than spot to process or process to spot conversions.
The auto-conversion from the Pantone to the RGB is slightly different:
This all may seem like it's being too meticulous. However, when you see colors next to each other, there are subtle variations.
There are differences visible in the image above, but they are exceptionally minute. A poorly calibrated monitor may not show them.
For me, these subtle variations are a great deal of WHY I'm picking colors. And I need to ensure that, given the variations, my client has access to the color I feel works best. So, to that end, I provide clients with CMYK, Pantone, and RGB files for their logo in every instance whether they know they need them or not.
If a client mentions something about why colors look slightly different, I then explain to them the various color builds and why some colors are not absolutely achievable in some color models. And I explain the efforts I take to ensure they get as close as possible in every use case and how it's just not possible to use Pantone colors on the web and for every print production run, largely due to costs. I also tend to only provide RGB color files if the client is approving digitally and only provide CMYK colors if the client is approving physically. Sending a client a CMYK PDF to view on their monitor is going to inevitably bring up the color issue. And sending spot color proofs will result in other issues depending upon what software they use to view the spot color proof (Apple's Preview application, and many web browser plug ins, won't render spot colors at all accurately in a PDF).
As for you printing Pantone colors to an Epson printer... well you aren't. Pantone is an ink system. Epson printers don't have Pantone ink cartridges. If you print a Pantone color to your Epson printer, it's being converted by the printer driver to CcMmYyK for printing, or even converted to RGB then converted a second time to CcYyMmK for printing.