What is the ruling on someone who prayed according to the North American prayer times found on the Islam Finder website, then discovered a time difference between it and another website that relies on the same calendar? Is his prayer valid, and is this difference merely a matter of precaution?

The fundamental principle for knowing prayer times is through the legal signs. If it is difficult to ascertain them, then it is permissible to follow reliable calendars whose compilers are known for their uprightness and trustworthiness. A Muslim should follow what he considers most reliable and should not pray until he is certain or has a strong presumption that the time for prayer has begun.