Do cats sense invisible energy which is unseen by us?

I can pretty much elaborate the nature technicality that why cats eyes glow in dark or why they shine or glow when you take a photo of them. It nearly happen to all the nocturnal creatures but specifically cats; the simple reason is which science defines is that cats' eyeballs include a special reflective layer called the 'tapetum lucidum'. The retina behind their pupils makes the pupil contract and expand when you get anything close or far to a cat while cat is watching it. In the day the cat's pupil is more dilated because it takes a little time to absorb the day light and hence there is no day-light at night cats tend to see better and are more quick and pro in glances. This is also the reason that we humans do not have that layer in our pupils so we get red-eyed in single flash cameras and cats' eyes just glow.
See my brother holding Fifi in the picture below. She is having that flashy glow effect in her eyes here.


Anyways this story is not about why cats don't have red eyes when photographed. I had a cat named 'Fifi' who was just a week old kitten when she came to me. I found her in my house street just a few steps away from my place and some crows had attacked her and pecked her one eye but luckily there were no injuries. I took her inside and washed her with warm wet towel, fed her milk and eye dropped her daily and after a week she was fit to see wide eyed both eyes. She was very cuddly, friendly and took me as her mother as I guess she wasn't familiar with the motherly love. The whole story short one day I found her acting completely weird which got me shocked too. I wanted to hold her and she ran away and got me running here and there and hiding under places and not letting me come near her. Then I cornered her in one place and observed that she was full wide eye with fear and was looking behind from above my shoulder. I looked back and thought may be someone else was standing behind me but there was no one. I tried to calm her and swoon her in low voices. When I got close her she hissed a big time and gave a constant gaze behind my shoulder and right at that moment I felt someone's presence right behind me. My heartbeat got faster though I am not the kind of kind of guy who get affected by any spooky environment but that day I could really feel someone was there. I do not know it was something bad or good but I got really scared. I just grabbed Fifi and got out of there reciting verses of Holy Quran. I had a mix feeling about having beliefs on this thing that cat can sense all this but I am not definitely sure about it.

I haven't let it out to anyone yet. Just today. Please share your comments and any experiences you have had like this. Thanks for reading!