White pixels left...

[Ofnuts]

Just a wikd guess: you are likely painting things on the same layer. Along the boundaries of the selection there are partially selected pixels (this is necessary for smoothness). You bucket fill the selection and fill one side: these partially selected pixels are partially painted. Then you invert the selection and paint the other side: these partially selected pixels remain partially selected (100%-partial selection is another partial selection) and so are also partially painted. And partial paint over partial paint is not fully opaque so you get the initial layer showing (or partially transparent pixels letting the layer below show through).

An example of what you would get with a 45° diagonal selection:

   

If you look closely, the pale squares have a blue component, that cannot be a blend of the pure red and pure green: this is the original white background which is not fully painted over.

This can be averted by growing the selection used in the first fill, so that the second fill's partially painted pixels overlay fully painted pixels from the first fill, namely:

• Create selection
  
• Select>Save to channel
  
• Select>Grow
  
• Fill green
  
• Restore selection from channel
  
• Select>Invert
  
• Bucket-fill with red
  

   

In the result, the transition pixels only contain red and green (and are a bit darker)

But in practice, you paint colors on different layers, and a square cut in half along a diagonal would be painted like this using two layers:

   

This produces exactly the same visual result as the previous solution, while requiring a lot less fiddlin,g woith selections.