When do customers actually receive reward points for an order?

Points are added when the order reaches the status you chose. Go to Plugins → Reward Points and look at Award points when order is in the Earning section. You can pick Pending, Processing, Shipped, Delivered or Completed. The default is Delivered.

With the default, a customer only gets points once you mark the order delivered. This stops points being given for orders that are later cancelled.

Also check that Reward Points enabled and Customers earn points are both ticked, and that Points per 1.00 spent is above zero. Click Save settings after any change.