Life cycle sounds about right. Around here, grubs feed for a short time in the spring. Then pupate. Emerge as adults. Mate. Lay eggs. New grubs emerge. Main damage occurs in October.
Japanese beetles emerge around June 15. Best time to treat, I have been told is about July 4th, --about when the eggs hatch. If using Acelepryn, treat a few days earlier as it is a bit slow to uptake--yet long lasting.