It's a world of difference between assigning a colour space and converting to it.
You should set your Photoshop or whatever software you deal with for image processing to warn about profile mismatches when opening a file. If there is a mismatch, select the best suited conversion method. 'Perceptual' often works well unless you have reasons for choosing the colorimetric variants.
While several modern browser are colour space aware, they often have severe trouble managing the wide gamut spaces such as Prophoto. Convert your image into a smaller and manageable space before posting the image to the web.