Display P3 to sRBG export - printed photos come out more saturated

@beatrizf32559652 you can make some saturation tests using this testimage, try I assigning sRGB - view onscreen, not good, right. Reset, now make a copy and CONVERT to sRGB - apearance is largely preserved expect in some very saturated areas.

Add a code on the image so you know which is which - Send both to be printed. 

please go here and download the Adobe RGB testimage

I hope this helps
neil barstow, colourmanagement net - adobe forum volunteer - co-author: 'getting colour right'
google me "neil barstow colourmanagement" for lots of free articles on colour management

Most consumer-oriented print shops don't have a properly color managed process. They basically assume sRGB, but even for sRGB files, don't expect a high degree of color accuracy. Some of them may even have auto-correction applied to every image. In short, all bets are off. 

If you send files in a larger color space, P3/Adobe RGB/ProPhoto, to a print process based on sRGB, you get a loss in saturation. You can mimic the effect by assigning sRGB in Photoshop. And in fact, that is what your example shows here, in print shop left vs. older print right. Although it's hard to judge which one is actually more saturated, as this is more or less a monochrome image.

I think you'd need to use another image with more color to make any judgements here. A blue sky usually gives a good immediate indication.

Or just ask them. If they can't answer, probably go somewhere else.

Is Display P3 really the image’s own Color Space?

Did you send it to the printers as such or convert it to sRGB? 

Did you embed the profile? 

Please set the Status Bar to »Document Profile« and post screenshots with the pertinent Panels (Toolbar, Layers, Options Bar, Status Bar, …) visible.

I know different printers will give me different results, clearly, but my question is: might this be a printer problem ONLY or could the problem be the picture profile I'm using?

If all involved parties employ Color Management the difference should not be a lot more than the gamut difference of the two Color Spaces – the image’s embedded ICC Profile and the physical printer’s Color Space. 

Did the printshop request sRGB?