Should I change my workspace colour profile to a specific colour profile from print company

@Maciej36501572k2yt Setting the default working colour space does just that, it's just a default. It applied to new emopty documents created in Photoshop.

I would prefer not to work on images after conversion a printer colourspace because it may not behave in. quite a linear manner. as @D Fosse advised you can use "softproof" with the destination set to the printer's Hahnemuehle colourspace (as defined by it's ICC profile) . Also check ink black there for better preview of the printed item.

It reads as if you have pushed those reds too far to be printed on that media, Photoshop's softproof and gamut warning are there to protect you from doing that.

Generally, the preferred setup workflow involves working on images in a decent-sized working colourspace like Adobe RGB (and activating softproof, also paying attention to gamut warning) - this allows repurposing of archived images for other printing processes down the line. If you want to convert to the printer's Hahnemuehle colourspace you'd better do that to a copy of your master file and archive the master in a working colourspace. Do not archive NOT a device colourspace. That way your options are open in the future as @Conrad_C explained. 

I hope this helps
neil barstow, colourmanagement net - adobe forum volunteer - co-author: 'getting colour right'
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If the colors are changing drastically, that is probably the normal limited gamut of a matte paper compared to Adobe RGB. If you convert to the printer profile earlier, this will not avoid the dramatic restriction of color gamut because the paper is never going to reproduce more color than a certain profile says is possible under that combination of printer, ink, and paper type. The only thing you will gain from converting early is that it will throw out the non-printable colors early so that you no longer be distracted by them as your frame of reference, so you won’t miss them as much. But any colors outside the color gamut of the selected profile will still be unreproducible and will still be thrown out at conversion time.

One major disadvantage of converting early is that if you convert before doing corrections, it is possible you will prematurely throw out color detail that you could have brought into the printer gamut if you had edited in the original gamut while viewing the image with the soft proofing simulation enabled.

Whatever you choose to do, the most important thing to remember is: Do not permanently restrict the original image to this specific limited color gamut. If you choose to convert to the printer profile, do it only on a copy of the original. If you choose to leave it in Adobe RGB and edit while soft-proofing with the output profile, add all color edits using adjustment layers so that they can easily be disabled. The reason for that is so that you keep a version that still has the original colors, in case you also want to show the image online while taking advantage of the larger color gamut of displays compared to print, or if in the future you want to print it again on media with a wider color gamut such as a glossy paper or a newer, better printer.

Although the following article is now 24 years old, it still holds true today for this type of work:

https://creativepro.com/out-of-gamut-soft-proofing-in-photoshop-6-0/

Normally not, you'd just soft proof and adjust as necessary. But if the gamut difference is dramatic, you might make a copy and convert just to have a little more control.

As long as your original master file is left untouched, do what feels best. Do they want you to deliver the file in this profile?

Note that you don't change the working space, that makes no difference - you Edit > Convert to Profile the document itself.