Why am I getting these white outlines when colour separating?

About spot colour and overprint:

https://helpx.adobe.com/photoshop/using/printing-spot-colors.html

To convert to other color modes:

https://helpx.adobe.com/it/photoshop/using/converting-color-modes.html

Well, color separating an RGB document is not going to be productive to begin with. You need to convert to a print color space (CMYK/Multichannel) and then check overprint and other settings. You may want to educate yourself a bit about some basics. If whoever is printing this wants this in RGB, then you may be wasting your time with unnecessary steps. Color separations often mean nothing for these workflows as e.g. short-run inkjet printing will simply rely on driver settings and the facilities color profiles.

Mylenium