The heavy offsetting season is, in my climate, during April and May. And then a smaller flush of offsets occurs in the August time frame. That's the short, simple, summary answer. But of course nothing is quite that simple. I'm speaking of the most common genus/species Sempervivum/Sempervivum. The Jovibarbas offset differently by rosette division and seem to be continuously but slowly happening in Spring through Summer. The Arachnoideums offset heavily in early Spring but in my experience not at all thereafter. The Globiforeums seem to be dropping little rolling offsets throughout the growing season. Offsetting appears to halt completely through the winter, even though I can see some slow growth happening in my mild winter climate.
The time chosen for a rosette to bloom is each plant's own private mystery. Sometimes an offset will bloom immediately without ever forming a rosette. Occasionally, immature rosettes may decide to take the plunge. Generally, though, each rosette will grow to a considerable size and then bloom. When they reach their maximum size you can expect them to bloom soon. Some species like Calcareum are shy about blooming, but most are not. And yes, environmental factors can play a role. Many of us have received a tiny offset hoping to grow a big plant only to have it panic and bloom, leaving us with nothing. Rarely and frustratingly, a plant may "bloom out" in which case each and every rosette blooms. But for the most part the larger rosettes are blooming with the smaller ones happily growing to replace them.