Over tightening could eventually lead to stripping. Also one needs to be careful when using metal screwdrivers close to strong magnets, one slip could lead to torn drivers.
Tightening Driver Screws
Every time I gently tighten the screws on my speaker drivers, I am quite surprised how effective it is. After about 1 1/2 years, I found about 15% were fully tight, 65% were slightly loose, and 20% were quite loose. Starting to fear I may have to look for the brass screws that some recommend.