Why do three series connected 1.2 V NiMH batteries read 4.16 V when charged?
No, that’s perfectly normal. See the charge curve for NiMH below. It’s about 1.45 V / cell fully charged. 
NiMH are tolerant to overvoltage as long as the current is kept low enough. This is commonly referred to as slow charging where the cells stay hot when fully charged until you remove them. Medium solution is higher charge current and thermal cutout. Any fast charger would need to sense zero delta V or negative delta V for charge termination. 
EDIT: Since you did measure that the charger bridged the two 3.6 V packs in series, forming a 6S1P configuration during charging, the 9 V and 0.2 A makes perfect sense. It’s actually so low “overvoltage” (9-6*1,45=0.25 V) I’m suspecting the charger is delta V sensing or “smart charger”. 
At least 1.1 Ah/0.2 A = 5.5 hours since they are charged in series to reach 80 % SOC. Probably +50 % more for 100 % SOC.