They do seem to have ESP, don't they?
But they don't. What they do have is EXCELLENT hearing so he could very well hear the car coming down the street before it gets to your door. He could also be 'reading' you and has figured out some sort of a sequence - like he knows that when you husband calls you on the phone or when you do something different (unlock the door? come downstairs? start putting dinner on the table?), his arrival is imminent. Parrots are not only prey animals (ALWAYS aware of what is happening around them because of the danger of predators) but also highly intelligent and masters of our body and oral language because they were raised by humans so it is entirely possible that you are doing or saying something that is just a little bit different and he is picking that up.
There is a famous case of a horse that could count, knew the alphabet letters, etc and for years nobody could figure out how the horse was doing it until they realized that the horse was 'reading' the questioner's face! He would look at the person who asked the question and figured out, by the person's expression, when it was the correct number of hoof taps (that was the way he communicated his replies). And I know for a fact that my animals (dogs, cats, birds) know how to 'predict' an action by the previous actions or words even if the action is not happening at the 'right' time. They also know when it's time for everything and would often let me know it's time for whatever - getting up in the am, going out, coming out of the cages, dinner, etc. The last dog I adopted is a 15 year old pitbull mix that got way too attached to me because she was abandoned in a basement for two or three months and severely neglected for many years before that (owner was a drug adict and would disappear for a couple of days at a time) so now she can't stand to be separated from me and goes completely out of shape crying, howling, scratching the gate, etc. Now, it is true that I am incredibly systematic in my routine so every day is exactly the same but she figured out in a matter of days that, after I put the gloop in the birds' cages, I put them in and immediately after that, I go outside to feed the street birds so, as soon as she sees me filling up the bowls with gloop and I start saying to the birds my usual "Uuuuuh, look! look! look! que rica papa!" (which makes several of the birds fly to their own cages), she starts carrying on as if she was being tortured because she knows that I will be going outside and out of her sight.
Observe yourself and see if you do not follow some sort of a pattern that he is recognizing because they notice the subtlest things, things we are not even aware of doing/saying - even tones of voice that are just a teeny tiny bit different.