The role of ethanol in the procedure is simply to "bleach" your sample (remove chlorophyll in the cell) so that it's easier to observe the precipitated NBT. Ethanol should not have any effect on causing the NBT to get darker.

In my opinion, there are 2 possible explanations for your situation.

First is that you didn't wash your sample with water to remove all NBT solution after incubating in step 2. This might leave NBT solution inside the cells of the sample, which was then continue to precipitate later on, causing more precipitation and darkening of the sample. To fix this, after step 2, wash your sample several times with water to remove all NBT solution before bleaching with ethanol.

Second is that ethanol causes the sample to loss water and shrink. In my experience, ethanol is actually not a very good bleaching agent for NBT/DAB staining. Ethanol evaporates very quickly after the sample is taken out of the ethanol solution, causing the sample to dry up significantly. This could condense the NBT precipitation inside the cell, making it appear darker. Instead of ethanol, you should try other bleaching agents. I found the solution of ethanol/acetic acid/glycerol, ratio 3/1/1, as proposed by Daudi and O’Brien (2012) give much better result as it doesn't evaporate quickly. Also, do not take the sample out of the bleaching solution until you are ready to observe to prevent drying out.