Here in the desert, they only offset in spring and summer. It also depends on the species or cultivar. They all offset in spring for me usually. Most of mine go dormant in the summer and just turn mostly green and sit there until the weather cools, but a few actively grow offsets for me in summer, especially S. tectorum and a few of my NOIDs. Kalinda also grows and makes lots of offsets in summer here. The small pot I got and up-potted a few months ago has grown pretty aggressively with offsets spilling over the sides already and a new batch coming out.
For me flowers only seem to happen to the biggest and oldest rosette(s) in a clump. So far! I've never noticed random incidents of blooming from differences in watering or anything. Age of 3 years or older in many cases and size seem to be the determining factors here.
