A cult of personality is a pejorative term for a group that idealizes a leader and subscribes to common political, social, religious, or philosophical beliefs. Personality cults typically have a few common traits, such as the idealized leader, patriotism, mass demonstrations, and distortions of the truth.
That said, it seems that TikTok cults, at least in this early phase, are mostly innocuous. Their followers will do things like change their profile photos to their leader's face, make absurdist videos praising them, and launch comment raids  on famous people's Instagram accounts.