I've had Lows I wouldn't categorize them as severe, however. My Basal requirements never completely settled after the first jab, but the second one has seemed to send me close to the normality of Pre-Jab 1. The lows were mostly caused by elevated Insulin doses now being inappropriate.
The only low I believe was actually caused by the jab itself (and others have reported this) is one within minutes of having jab. So make sure you have a hypo treatment/proper test kit ready to check yourself after the jab. In my case, it was almost instant, like walking out of the Vaccination Centre I could feel it happening.