Maja,
As I now (mis)understand it, you are working in black first (artwork in black on an apparent white background), then you are supposed to have it in white on a black background, and lastly in colour on a white (apparent) background; then export it as a set of TIFF files.
If so, you may, after having completed the artwork in black (which I guess you have):
1) Create an Artboard the size of the TIFF image and create a white rectangle filling the Artboard, beneath the artwork (you can select it and Ctrl/Cmd+X+B);
2) Copy the whole thing twice to new Layers (so you have 3 Layers);
3a) Select everything in Layer 2 (presuming you have black artwork on top of a white rectangle) and Edit>Edit Colors>Invert Colors, or
3b) In Layer 2, select everything and in the Window>Transform palette flyout (click the right arrow) click Make Opacity Mask with both Clip and Invert Mask unticked, then change the colour to black;
4) In Layer 3, (re)colour the artwork as desired, selecting and working on each object (set) at a time;
5) For each layer, export to TIFF.