It has been a while since you asked the question. If you're still looking for an answer, let me try to provide one:
tSQLt is in part based on CLR code. As such, you have to enable CLR on the instance in question. The newest version of tSQLt does not require any additional changes that could affect security.
However, to execute tests, you likely need db_owner permissions, as tests regularly create and alter existing objects in the database.
So much for security. However, and in general, I do not recommend installing tSQLt in a shared environment. While it should not cause security problems, because it is not really thread-safe it could cause other headaches best avoided.