How to prevent Photoshop from auto correcting the colors of my images

No. A simple no.

since no one answered, I will answer for it (soooooo late, but I just found it)... here's the screenshot, but since I'm abroad for a while I just have a random laptop display, so color fidelty could be really low...but they still look different to me...

BTW since non one explained it correctly, you can consider Photoshop as filtering the original color profile through the ICC profile of your monitor (said with an extremely easy explanation)...I had the same problem on this image:

I rendered it from C4D with an sRGB profile and tweaked on Nuke (that don't have color managing) then tried to upload it on Firefox and it turned purple! so I imported it in Photoshop to see what was going on and it was purple as well... (don't really have a screenshot for that...) but that's because Ps, as well as the browser, was reading the ICC profile of my Laptop (yeah, I know I shouldn't argue about colors from a laptop, but this is the situation at the moment) and tweaking the sRGB to make colors display as they are supposed to be...but what's the story? well, since I had the WHOLE process before Ps on a non-managing colors applications (my first render was even in .exr, which uses a linear color space) I tweaked everything on a non-filtered sRGB profile, this means that once my ICC profile was read, the colors on Ps got a mess, because they weren't those seen until that moment...and guess what? if I was assigning my ICC to the image color profile, it displayed correctly...

Ok, I think we're on the same page. There's been a lot following from your initial and very clear assertion that this is a Photoshop bug, and hence people have put a lot of energy into proving that it isn't. But what matters is that you see this image with the colour mix you like, and you want to get into Photoshop what you see. And, presumably, go somewhere from there - make something in Photoshop from that image, and also see it as you want. That could be harder. As you've found, you can tag the image with the monitor profile, and you see what you want in Photoshop. But people are drawing your attention to this having problems later, and probably looking even less like you want.

Now, I'm stronger on theory than practice, but perhaps people can critique this idea.

1. Get the image into Photoshop.

2. Tag it with the monitor profile [since that is the profile needed to get the colour balance you want].

3. Convert (not tag) it to sRGB.

This sRGB image is probably (it seems to me) your best shot at an image which will look reasonably consistent on YOUR system. If your monitor is calibrated, it may also look consistent on other people's calibrated systems. Any comments?

I took a closer look at the two screenshots.

Assigning the "other" profile to each does not produce the expected match. There's still a difference. So that's not it. In addition - NA general purpose has sRGB as working. So that would produce the opposite result if the file was untagged.

So I'm back to my original theory: Photoshop is using the wrong display profile - whether on its own, or it gets that profile from the OS, or it's Mac OS doing it on its own. All three are just as likely (except on Windows the third would be impossible).

But we still haven't heard back from the OP, as to whether this is in fact a dual display setup, and if so what particular displays are used.

I suspect that it happens when there is no color profile tagged in file and it differs from working profile and the warning is turned off. Then PS assignes working profile to image which is made with another profile.

Please check policies for "profile mismatches" and "missing profiles". I'd check also the pasting. They are all good to be checked.

Converting won't matter. It will display the same. This is a color managed application, which displays everything correctly whatever the document profile.

This is most likely, yet again, a display profile problem. Probably not a corrupt profile, more likely just the wrong one.

Is this a dual display setup? If so, exactly what displays are used (make and model)? This is what it would look like if the display is wide gamut, but the application uses an sRGB-type display profile for it.

Check Edit > Color Settings. Color management may be converting images to working RGB without asking.

Looks like the image has the AdobeRGB profile assigned. If that's the case, then the image on the right, in Photoshop, is the correct colours (as intended by whoever assigned that profile). If you prefer the appearance on the left, Edit > Assign Profile, and try assigning sRGB.

Check if you've on the soft proof. Press Cmd/Cltr + Y to enable or disable it.