You raise a particularly interesting question, and the answer (I think) has to do with the structure of the food coloring dyes used.  

Currently (according to wikipedia) there are seven dyes that are permitted in food:  these are

FD&C Blue No. 1 / Brilliant Blue FCF, E133 (Blue shade)

FD&C Blue No. 2 - Indigotine, E132 (Dark Blue shade)

FD&C Green No. 3 - Fast Green FCF, E143 (Bluish green shade)

FD&C Red No. 40 - Allura Red AC, E129 (Red shade)

FD&C Red No. 3 - Erythrosine, E127 (Pink shade)

FD&C Yellow No. 5 - Tartrazine, E102 (Yellow shade)

FD&C Yellow No. 6 - Sunset Yellow FCF, E110 (Orange shade).

Now if you look at their structures (to the right) you will see that they all have aromatic (alternating single-double bond) rings and chains, which would normally be considered hydrophobic (water insoluble).  But, because they also contain lots water soluble groups (like OH, SO) they are (somewhat) soluble in water. 

Now the potato cell (below) has both hydrophilic (cytoplasm) and hydrophobic  (membrane interior) components.   You add dye to the water and you find that it concentrates in the cells. 

In fresh water, there is a net flux of water into the cell, because the water concentration inside the cells is lower than it is outside.  In salt water, there is net flux of water out of the cells, for the same reason - the net flux will be in the direction of higher to lower concentration. 

But the dyes have different molecular properties than water, they can behave differently.  It is possible (and likely) that some of these dyes will be more soluble in the potato's cell membranes than water, or that they may bind to molecules within the potato cell (this is the logic behind cytochemistry which uses various dyes to stain specific parts of a cell or specific molecules within a cell).

If this is the case with the food colors you used, they should concentrate in the cells in the absence of osmotic effects.  You could test this hypothesis by dissolving the dye in an isotonic solution (where there is no net flux of water into or out of the potato cells).  If the dye favors the potato, that is if it binds to molecules in the potato cells, or dissolves into the membranes of the cells, it will concentrate there. 

There is a discussion of solubility at the biofundamentals web site: here