A Problem for Color Management Experts

It looks quite simple really. The colours you are creating do not fall into the CMYK printer profile that the printer has provided.

you can soft proof to see how they look visually in photoshop before printing using the profile provided.

Also sRGB is a divice profile for representing colour on a monitor for instance, it is not a working space.

if the printer profile does not replicate the colors you see there is nothing you can do about it, you will have to manually adjust the colours youself so they fall within the printer profile.