First, magmax calculates the distance modulus for the given redshift and cosmology. This is done by a call to the function calc_dm. For further reference on this function, check its documentation on the groupwork page, http://panisse.lbl.gov/groupwork/documentation/cosmo/index.html
If the given cosmological parameters describe a bouncing universe, calc_dm returns -1000 to magmax and magmax then exits by printing an error message and returning -1000. If the calculation of the distance modulus was successful, magmax calls a C function in the library file magnitude.so (for further reference on the C code and the IDL function CALL_EXTERNAL, see section 2.5 below). The C function reads in a supernova spectrum at maximum light and then flux calibrates it. Then it reads in the filter. It then redshifts the spectrum and integrates the spectrum with the filter. The result is converted to magnitudes and then the distance modulus is added. After that the result is returned to the IDL function magmax.
By choosing this way for calculations, no explicit K corrections are needed. Filter mismatches don't occur, the only possibility for a filter mismatch is that the filter doesn't match the spectrum at the given redshift, which is treated as error. Corrections due to cosmological effects aren't necessary either, as calc_dm calculates the distance modulus from the luminosity distance, taking all relevant cosmologial effects into account.
Also, as better spectra become available, the program can easily be updated by just plugging in another SN spectrum. For instructions on how to do this, see section 2.6 below.