Consider that the word caution has both a noun and verb form, so there are multiple proper uses depending on where you place it grammatically.
Looking at your example, you have used it as a verb. The object in your sentence is “the fact.” Can a fact perform the action of cautioning? You see, this doesn’t really make sense. But a fact can give your some sensation. The fact that it is daytime can cause you to expect warmth, for example. So a fact can give you “caution” (the noun form). It can also “make you cautious” (the adjective form), or it can make you “proceed cautiously,” the adverb form.
When you want to use it as a verb, remember it is an action word. The subject has to be able to do that action. Can a dog caution you? Maybe, let’s try it:
“A big dog cautioned me against moving any closer.”
Well, that can work if your writing a comedy or have speaking dogs. But a feature of the dog certainly can do this more plausibly:
“A growl in the dark cautioned me against moving any closer.”
Build your sentence generically, then choose the most effective form of the word for the effect you want.
- Bob cautioned us not to go into the house (v.)
- Bob’s tone gave us caution against going in the house (n.)
- Bob urged us to go into the house cautiously if we had to do this. (adv.)
- Bob told us to use caution when going into the house. (n.)
- Bob’s warning made us cautious about going into the house. (adj.)
- The house made us cautious after Bob’s dire warning. (adj.)
The proper “preposition” then (that only applies to the noun form, factually) will be determined by your scene. Specifically; where do you want your reader’s “eyes” to be focused.
If the scene needs the readers to:
- Focus on Bob, then “Bob cautioned…” (you have told us how Bob acted)
- Focus on Bob’s behavior, then “Bob’s tone gave us caution…” (you have given Bob’s behavior a description)
- Focus on ‘our behavior’, then “… urged us to go cautiously…” (you have given ‘our behavior’ a description)
- Focus on ‘us’, then “… made us cautious…” (you have given ‘us’ a description)
- Focus on the house, then “The house made us cautious…” (you have told us how the house acted)
So decide where your readers need to be looking. Choose the preposition or adverb or other modifier that puts that on center stage.