They can. This one seems pretty mild, I haven't seen anything that's actually affecting people. Last one made people transform into other species. The one before that, everyone within the Fissure lost one of their senses.

[Just as calm, though his voice does take on a slightly displeased tone. He hadn't liked the sense loss Fissure at all]

The effects aren't permanent at least, though sometimes aspects can stick outside of the Fissures. I can still transform into the form I got last Fissure, if I wanted to, for example.