Is there a big color difference between the digital proofing before printing and the final printed product?

There must be some mistakes. Moreover, the principle of digital proofing is to use inkjet, but printing is different. So I suggest you use a color separation (electric color separation), which has different names in different places and is also part of printing.

The principle is the same as printing, and it is also done by printing film, which is generally suitable for color matching in printing. Now our master prints color matching. If there is such a thing, he will print his finished product with CMYK in this electric distributor.

But I suggest you use AI\PS. These two softwares are similar to printed ones.