RGB and CMYK are two different colour spaces. RGB is meant to represent the colours that can be produced with light using Red, Green and Blue dots. CMYK is way more limited. It is meant to represent colours that can be created with ink, but not with any ink but specifically mixing Cyan, Magenta, Yellow and Black.
The RGB space and the CMYK space have different gamuts. This means that there are colours that can be represented with RGB that cannot be represented with CMYK. Not every colour you can see on the screen can be printed using CMYK inks. Some are impossible to print.
The opposite is true as well, although to a lesser extent. A few CMYK colours are impossible to represent in RGB.

Image Source
When you set PS to CMYK mode, it restricts itself to work within the gamut of CMYK. This means that when you modify the colours it only creates results that can be printed, not colours outside the gamut. In particular, when you create CMYK gradients, PS tries to make sure that the gradient is printable from beginning to end; that every single spot of the gradient is a CMYK value that can be printed. It does this by reducing the amount of ink that needs to be used. In your case it goes from the CMYK value (4, 98, 88, 1) which is the CMYK version of your RGB colour, to (0,0,0,0), no ink at all. Probably it tries to make sure, as well, that the ink density decreases the same way for all inks. Not sure about this though.
The same gradient created in RGB mode has way more flexibility. PS can create a smoother gradation because it has more colours to choose. The result is that PS, in trying to make a nice gradient as smooth as possible, takes a completely different path while gradating from #de1f26 to #ffffff because it does not have to avoid unprintable colours.
Take a look at this image, for example:

The file at the top is RGB. The one at the bottom is CMYK. I started with the same colour in both cases and decreased the opacity of the circle in 25% increments. Notice how the colours that result are completely different in both cases.
Take a look at this now. This is the colour composition of both images, side by side. The first one is the RGB image and the second one the CMYK image.

Notice how, in the RGB image, the colour starts with no so much red but lots of green and blue. To create the gradient PS cannot play with the red too much, since there is not much to start with anyways, so the only thing it can do is to reduce the blue and green progressively, traversing through cooler colours (little red, lots of blue and green).
The CMYK image, though, starts with lots of Magenta and Yellow, but little Cyan. To create the gradient PS cannot play with the Cyan much, so it reduces the Magenta and Yellow, traversing through oranges (little cyan, lots of Magenta and Yellow).
Mind you, to make things way more confusing, the CMYK colour you see in PS is not a true CMYK colour, but an RGB representation of the CMYK colour. PS tries to make the best it can to represent how the colour would look if printed. The RGB colours, though, are true because the computer itself uses RGB.