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Just using the conversion from RGB to CMYK in Photoshop will not guarantee good color conversion because there are so many RGB colors that are not printable using CMYK.
That is why you need to have a calibrated monitor so you can see with your eyes what colors change when you do the conversion.
Exporting to tif, or jpeg has nothing to do with color, other than a jpeg file can have more hi-light loss due to clipping from file size reduction.
Monitor calibration is very important. If you can accurately see the color before you print and it is wrong - you can fix it.
See the attached color settings jpeg.
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