The keyword to search for, if you are interested, is epigenetics. Modification to e.g. histone protiens can change the expression of genes through a variety of mechanisms. As far as I'm aware, exactly how this works isn't that well understood.
Colistin has a pretty interesting mechanism of action, disrupting ionic balance in cell wall of lipopolysaccharide.
The mechanism of resistance may well be lucky upregulation of ionic balance and cell wall stabilization proteins in response to the attack. Same as for lysozyme.
This kind of ionic environment has wide ranging effects on cell metabolism so changes genre expression. In multiple generations, the resistance might get baked into the genome...
Good point :).