You should not use Photoshop anymore to import or export your images in TGA. Since Photoshop CC, the alpha channel is no longer saved in TGA. Maybe there are some scripts to fix that and export in TGA with alpha channel, but I never found one myself, so I'm just saving the image in PSD or PNG, open it with Gimp to properly save the image in TGA. Gimp saves in TGA with the alpha channel.
The alpha channel stores the transparency datas of the image.
Unlike an image in PNG for example, the TGA format stores the transparency values of the pixels in a separate channel (using a fusion mask on your layers is the usual way to affect the alpha channel of your image). But that's an option, and you can save in TGA without the alpha channel. And as I said, Photoshop doesn't give you the option anymore : no alpha channel with TGA. (the alpha channel is merged, and pixels who should be 100% transparent turns opaque white)
When converting your TGA to BLP, software like Warcraft 3 Viewer warns you that your TGA doesn't have any alpha channel and will add one for you. But it'll be an alpha channel 100% white (white = opaque), so no transparency.
- If you want to export an already existing texture like in your case, open the TGA directly in Gimp, and either do your things in Gimp, or export it in PSD (Gimp can do that perfectly), open the PSD in Photoshop, save it in PSD, open it in Gimp, and export it in TGA.
But it doesn't explain why you have an issue with your teamcolor. In War3, the teamcolor consists of a separate material using a ReplaceableTexture. Where the teamcolor is displayed on a model is not stored in your "real" textures. So either you're just confused with the render of your texture because your TGA has no alpha alpha, or you have two separate issues.
I can illustrate my explanation with images if you want.