I am not familiar with those Apps, but the same general rule applies with most transparent web logos - you need to have a transparent background to begin with and you then export the file as a .png or .gif file.
If your logo does not have a transparent background and is currently a flat jpg image with white background, you could bring it into AI and apply a Live Trace to make it a vector or you could go to "Create Outlines" or "Outline Path" in AI to get rid of the white background.
Then it is a simple export through AI to a .png file.
In my experience, a .png file will give you smoother curves then a .gif.