The mind is a strange thing. Take Dejavu. This is a glitch of the mind where your visual centers are moving slightly behind schedule and the light data reaches your short term memory "before" they appear on screen for you!
So when you "see" it, its already been chewed on by your short term memory and creates that momentary state of familiarity and confusion where you are SURE you've seen it before.
When in waking life and FAMILIAR terrain, your mind creates nearly everything you see from memory in order to conserve computing power. In otherwords, your tunnel vision is decoded light-data, but everything around is a fragment of memory. Thats why its so very easy to miss things in your perephrial vision that shouldn't be there. Knowing this I used to scare the crap out of people all the time by holding still while they walked right past me. I am invisable to their preferial vision because they didn't look directly at me and the perefrial was being constructed by the mind.
When you are in unfamiliar territory, your brain is working harder and translating everything around you from light data, even perefrial vision. Thats why you seem so much more "alert."
Consider dreams. You dream about strange places and settings. Your mind is in a perpetual state of creating imagry that is unfamiliar, yet "feels" familiar. Because the brain is working hard, but isn't completely turned on, I "theorize" that is because a lot of that info is hitting the short term memory before being projected up on screen for you since the brain is lagging a bit. That may be why everything seems to feel alien but "familiar" in a dream. You're in a perpetual state of dejavu.
SO the point of all that is... it is not at all unlikley your actually felt the fear first, but the visual representation and cognant recognision of fear was lagging behind the actual feeling so that it would "appear" you saw the entity first.
The mind is a strange and wonderful computer. But like all computers, its got its glitches. Some of those distort reality. Especially our perception of the flow of time. The world is filled with people who bleieve they can see the future because they experiance little blurbs like this, and wonder how they knew the phone was going to ring. Trouble is, lacking the ability to dig for the answer with thier human reason, many just break out the ol' supernatural stamp.