A cult refers to a group of people who share religious or spiritual beliefs, especially beliefs regarded by others as misguided, unorthodox, extremist, or false. Such people usually hold their meetings secretly. All cults are secret societies in this context.
It follows that "secret cult" is a tautology - it is tantamount to a repetition when we combine the two lexical items.
Always say "cult" whenever you want to refer to the erroneous "secret-cult".