Screens mix light (RGB); printing mixes ink (CMYK) — which is why printing works in CMYK: it's the four-ink set that reproduces colour consistently on paper, the same way on every press. Some bright screen colours — vivid greens, electric blues — simply can't be mixed in ink, so they print slightly more muted. That's physics, not a printing error.
What happens with your file at HelloPrint: if it arrives in RGB we convert it automatically using the FOGRA standard printing profile, and flag the conversion in your proof's pre-flight notes — so you judge the result on the proof before approving.