Why can the same Kp index, the 0-to-9 number that rates how disturbed Earth's magnetic field is, mean a good chance of seeing an aurora in one place and almost none in another?

Answer: Latitude still decides how far the aurora has to spread to reach you

Latitude still decides how far the aurora has to spread to reach you ✓ — Correct! Kp measures how stirred up the whole magnetic field is, not where the aurora will hang. Auroras normally sit in a ring around the magnetic pole; a higher Kp pushes that ring farther toward the equator. A town already near the ring needs only a small push to be under it, while a city far south needs a rare, strong storm, so the same number means 'likely tonight' in one place and 'maybe a glow on the horizon' in another.

Local air pressure sets where the aurora can appear — Wrong. Air pressure drives weather, not auroras. The lights form a hundred kilometres and more above any weather, and how far they spread depends on the magnetic disturbance and on your latitude, not on the barometer.

The size of your city matters more than the index does — Wrong. A city's size has no bearing on where auroras occur. What big cities do bring is light pollution, which makes a faint aurora harder to see, but that changes visibility, not the aurora's reach.