Several reasons can generate negative uV-VIS values for the dye. One of these reasons is problems with the baseline. Negative fluctuations can occur in the spectrum when the correction is not done correctly. It would be best to check that the blank you use is correct for your sample. Another problem may be associated with the concentration of the dye, since in concentrations with absorbance close to zero, there may be a predominance of noise. The same can be observed if the material is excited in a region of the spectrum where the dye does not absorb well.
To identify the real reasons, it may be interesting to check that the dye has dissolved in the solvent, which will reduce dispersions, and that the optical density values are between 0.1 and 1. If the optical density values are too low, measurement noise may be influencing the baseline. It can also be useful to check that the cuvette is free from contamination.