Indeed, the causative form can mean "to cause something to happen" in intransitive verbs (e.g. 空が曇る --> 空を曇らせる), but the transitive counterpart is usually used for that meaning when it exists. For instance, 木を燃やす is used instead of 木を燃えさせる, and the same goes to 岩を落ちさせる vs. 岩を落とす, 氷を溶けさせる vs. 氷を溶かす, or 湯を満ちさせる vs. 湯を満たす.
As you might realize, these -す ending transitive verbs have relation to causativity or agent's volition. Actually, す is a classical auxiliary verb for causative, corresponding to せる/させる in modern Japanese. These transitive verbs are originally from the causative form of the classical verbs 燃ゆ, 落つ, 溶く and 満つ, respectively. The intransitive counterpart 燃える, 落ちる, 溶ける and 満ちる are also from the same etymologies, of course.
We have a thread about this topic. See the following thread. (It's a bit long since it includes numerous example sentences. You can ignore them.)
causative form | Japan Forum
Confusingly, the meanings are not always the same between the causative form of intransitive verb and transitive verb especially when the causee/object is animate.
e.g.
犬を机の上に乗らせた。
I made/let the dog get on the table.
(The causer is the speaker and the causee is the dog. Thus, the agent of the action "to get on" is the dog.)
犬を机の上に乗せた。
I put the dog on the table.
(The agent is the speaker.)
Note that 乗らせる is really used, but another expressions such like 乗るようにさせる or 乗らせてあげる are more common. Plus, 乗せる can also works as causative of the intransitive action "to make/let get on", as mentioned in the thread I linked above. Similarly, 自分で起きるようにさせる is more common and natural than 自分で起きさせる.
