Why is my sample print coming back as oversaturated and darker even though I used the correct ICC profile they gave me and edited my photo accordingly?

A company is selling my prints on my behalf and gave me an ICC profile to use which is ‘Sihl Hot Press’. I installed it on windows, used it as my proof set up on photoshop and edited the colours accordingly to the original file until I was happy it matched the physical photo/the SRGB file and so on. Everything matches and I did everything they said to do correctly. Even on the preview it looks exactly how I wanted it to look.

They sent me a sample and the colours are horrifically over saturated and darker and I don’t know how to do any more as I’m not educated on this area.

What can I do? Shall I simply just desaturate it even though the file will look slightly greyed out on my end and just hope it looks more true to my original file?