Your grandfather has already tried to warn you guys when he's about to arrive, but he feels like he "just knows" anyway?
Well, there are some pretty scientific explanations for that. We pick up way more information than we're consciously aware of - sounds, smells, changes in routine. If someone always shows up around a specific time, your grandfather is processing those patterns automatically, without even noticing. There's also the selective memory factor: we remember when we get it right, but forget the days we got it wrong. If he was wrong 3 times and right 1 time, you maybe only remember the one he got right.
Another important thing is intuition itself, which isn't mystical or anything - it's your brain connecting dots fast. Could be a phone call you got a few minutes before, a shift in people's mood around the house, even the time someone usually shows up. All that together creates a feeling of "certainty" that seems magical, but it's just cognition working behind the scenes. Sixth sense is a cool way to call it, but basically it's just your brain being really efficient.