Hi, sorry to hear that, I presume it may be a codec issue. You could try interpreting the alpha channel with the file as either straight or pre-multiplied within Avid, if that does not help, I would suggest you re-encode the .mov file, here is an excellent and free encoder;

Just import the .mov file into that program when installed and convert it into a format, remember to choose an output format that includes an alpha channel! Perhaps as .tifs or .tga files (RGBA/millions of colours+)