Clearly not. Manuals are often written with errors and now one cares. The slit widht is proportional to the bandwidth until you reach the diffraction limit. The figures could refer to the actual physical slit width if micrometer and nanometer is confused.

The slit width settings of 2.5, 5, and 10 nm on your spectrofluorometer refer to the spectral bandwidth, not the physical slit size. Narrower bandwidth means higher resolution but lower signal, while wider bandwidth increases signal at the cost of resolution.