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If there is a tint, and there are no out of gamut colours, then it is your screen (lack of calibration), or the rendering intent. Perceptual will shift colors, even if there are no out of gamut colours in the image. Relative colorimetric will only shift out of gamut colours into gamut, any in gamut colours will remain constant. Try toggling between the two intents; if the tint occurs with both, then it is your monitor that is the problem.
The only reason to use perceptual would be when you have out of gamut colours; or, if you don’t have the time to examine an image to see if there are out of gamut colours, which is generally the case for large print shops. It is one of the reasons why small custom printers cost more money.
With soft proofing checked in the Lr development module, and the correct output profile selected under the histogram in the left panel, there are two small buttons in the top corners of the histogram. The left one will toggle what is out of gamut with your monitor/graphics card, but is meaningless unless you have calibrated your monitor and built a profile for it.
The one at the top right toggles out of gamut colours for the output profile; they should show up bright red in the rendered screen image. If you are seeing just a few scattered pixels out of gamut, there is little point in messing with the image.