Help me solve alpha compositing algorithm in c++

I am working on a plugin for Adobe After Effects that performs a blur. When the image has an alpha channel, it is blurring incorrectly. This is because it is blurring with the colored pixels that lie on the alpha=0 sections. I have created and attached an example to illustrate. In the top-left image, we have the original. It has an alpha channel but I have it disabled. In the top-right image, I am importing it with the alpha channel. It displays the pixels in the alpha channel section as black. In the bottom-left image, I have performed my blur algorithm. You can see that the edges have a bright halo because they are blurring against the light colored background pixels shown in the first image, even though the alpha channel is there. In the bottom-right image, I have composited it against a background so that you can see it is compositing incorrectly. I have read that this might be an alpha premultiplication issue, or an alpha gamma correction issue, or both. I have tried premultiplying the RGB pixels that lie on the alpha=0 sections by black but it is still incorrect. I have an example I can show that produces correct output. I am looking for someone who is extremely well versed specifically in computer graphics imaging and algorithm using C++. You should have experience and understanding of what I'm describing in order to help. You will be required to show work you have done in the past that proves you understand alpha channel compositing. PLEASE DO NOT BID ON THIS IF YOU DO NOT HAVE EXPERIENCE. You will have to log in and work with me via TeamViewer. I appreciate and am looking forward to any help on this as I'm really stuck! I will most likely have other issue I'll need help with as well.