I do not mean to be rude, but your process is wrong on many levels.
But If you are really panicking, Don't. there is light at the end of the answer.
or there is something called ICC profile I used without even knowing what that thing is
So, How did you convert it to CMYK in the first place, because the conversion totally depends on that little thing called ICC profile?
I sent the prepared-for-print image
It is not prepared for print. You do not know the conditions they will be printed on, so the file is not prepared for that. That is what a color profile is needed.
Did you prepare the final project on Ps? I hope you have the dimensions right. Do you know about the resolution?
Did you prepared the file as RGB or CMYK, so do you know the maximum ink values accepted?
I wanted to use .tif
Why? Probably because you heard that is a format for printing... But you need to understand what is really needed for printing, and this file format is not "needed" in this case.
I sent the prepared-for-print image to my boss and when he opened it, the colors were reversed. He used a program called IrfanView
There is no program on the planet that I am aware of that reads a CMYK file "reversed"
Here is a program called Irfan View with a CMYK file that is not reversed, you can see the data on the information window. CMYK, Resolution, Compression. And with the colors pretty much OK.
But even in that case, why your boss needs to view the print-ready file when he is not using software to view a print-ready file? Why do you even send a print-ready file for review when you should send a preview file for approval, and then send a print-ready file for print? Why you do not know what software the other parts of the process are using, especially on your workspace?
If I should save layers, too or without them is okay
Why would anyone need layers for a print-ready file? A print-ready file is a file fixed, not to be edited in almost any way.
So... What is happening?
What Irfan view does not do well is reading the color profile of a TIF file. and it oversaturates it. But the colors are not reversed.
That is what a color profile does and why it is important. It tells, not only the ink values but "how are they supposed to look" on the medium you are printing.
But the good news is that that way you can be sure it is a CMYK file. n_n
What to do:
- Ask for the CMYK profile. If they do not say a word, use a generic one, but USE ONE.
Fogra 39 is commonly used for Digital print. If the printing company has no clue or just says "whatever" yes, just use it.
Confirm the resolution. For a digital banner, 150 PPI is fine.
You do not "need" to send a Tif file. A well prepared JPG file in CMYK color mode is fine. The "Maximum" quality slider in Ps uses a quality level of 10. Slide it to 12.
This JPG can be read properly in Irfan View, but most importantly it is a good format for a digital print.
- Please, study about color profiles, and how to properly send a print-ready file. There is so much more, that has to be done in a file.
What you should do next time?
Assemble the file in a vector-based program, especially the texts. You need to understand the differences and usage of them.
Export the file to a PDF file, text converted to curves. (This is a format that also needs to be understood, resolution, compression, color profiles, color conversion, font management)
Tell you boss to use Adobe Reader.
In some other cases, for digital print, they do not ask for a CMYK file, because the conversion from the RGB file is made by them with the specific color conversions, that in my opinion, is the right approach.