Anne,
You might want to stick with TIFF. FrameMaker cannot output CMYK, only RGB. So, if your TIFF is in CMYK, Frame might convert it to RGB. And Frame does not handle color management to my knowledge.
That being said, I do not know how Frame handles TIFF images. I always use eps for graphics, especially Illustrator graphics, because Frame just passes eps files through to the printer or PDF creator, whether the eps file contains CMYK or RGB or something else.
Of course, the above is not the definitive answer, but it might help. I have no idea why the image would invert color.
Van