The hemisphere of origin does not change whether a plant will be active or inactive during summer. A plant does not have a "memory" of what half of the planet it came from... if you moved a plant from (say) South Africa to (say) California, it would be confused for a while (maybe the first couple months) and then resume its normal seasonal behavior, to the extent it had seasonal behavior to start with. Maybe it would skip a flowering season or flower off season its first year.
There was a list of summer growers and winter growers circulating on the internet a few years ago, and though it was mostly inaccurate, it was useful as a point of departure. Summer dormancy depends on the climate of origin, specifically its seasonal rainfall pattern, but cannot necessarily be predicted from that.
Aeoniums are (mostly) from the Canary Islands, which have a Mediterranean (winter rainfall) climate pattern, and they are winter growers. So is Senecio kleinia, a deciduous succulent shrub, which loses all its leaves in summer.
The winter growers around the planet come from Mediterranean (winter rainfall) climate patterns, which exist in about 5 different locations globally. Outside the Mediterranean itself, they tend to be on the west side of continents in the subtropics. They exist in Mexico (ie. Baja California) and the succulents from this area are either year round growers (no dormant season) like our native Agave shawii, or they are winter growers (summer dormant) like our native Dudleyas.
The greatest diversity of winter rainfall succulents comes from South Africa, which has summer rainfall and winter rainfall (and mixed) zones. The west coast of South Africa has winter rainfall, with increasing aridity as you go north. The more arid the climate of origin, the more likely the winter rainfall aspect will dominate a plant's growth in a more forgiving climate. Some examples of winter growers (summer dormant plants) from South Africa include Tylecodon, a whole genus of succulents that lose their leaves during summer; and Pachypodium namaquanum, the only member of its genus which goes deciduous during summer and experiences most of its active growth during winter. Both of these would be terrible ideas for climates with lots of summer rainfall. I know people who have tried and were disappointed.
The important distinction here is between hard wiring (so-called obligatory summer dormancy) and responses to environmental stress (eg. summer heat and drought). Not all plants from winter rainfall areas will be hard wired to go dormant during summer. They will usually be opportunistic in their growth pattern and keep going when conditions are favorable (as they generally are here, at least on the patio).
As for which plants go dormant in hot weather, that probably would apply to lots of plants which do not necessarily come from winter rainfall climates, but for whatever reason do not tolerate heat very well. (Maybe they come from high altitude.) I would not treat the groups as equivalent, though the end result may be the same in a hot climate.
A long answer and more than you wanted to know...
