The offsets from your Big Blue are clonal. Most hybrid semps are stable in reproducing by offsets. That does not apply to the seed they produce.
There are a few semp varieties that can have a tendency to be unstable, producing non-clonal offsets.
One would be Fame Monstrose:
Hen and Chicks (Sempervivum 'Fame Monstrose')
Oddity is another one. It can produce normal and quilled offsets from the same rosette.
Hen and Chicks (Sempervivum 'Oddity')
Another reason they are so fascinating.