But were you using Absolute intent? This is the only thing that makes sense from your post.
Relative or perceptual intent should give similar results if Black Point Compensation (BPC) is available, relative might offer a fraction better contrast at the expense of some finer colour differences in highly saturated areas compared to perceptual. If there is no BPC option, then Perceptual would be the better choice than relative if there is any shadow detail.
EDIT: If an image has had JPEG compression then the white areas may have "scum dots" and may not be pure white.
I was using Relative, but it also happens when using Absolute or Perceptual.
I think the real problem is in the Hiipoo ICC profiles. The Hiipoo Ink is sublimation ink that prints unto sublimation paper and is then heated to sublime the ink onto a substrate (ie coffee cups, tumblers, etc). Using the color profile from the ink supplier is supposted to give acurate colors onto the substrate (the paper prints look more faded and off color). The problem I am having is that the Hiipoo ICC profile for my printer (ET-2850) gives a silghtly grey background instead of white (L=98 instead of 100). Since my sublimation is onto white substrates, white is just areas where no ink is printed (there is no white sublimation ink). This ET-2850 profile is printing a greay cast where it should be blank (white) which shows up as a grey box arround my design.
I tested all of the Hiipoo Ink EPSON ICC files and have found that using the ET-16650 ICC profile (printing Relative) gives me the closest color match to the ET-2850 (delta E of 3.7), but with a white/clear background.