The Flexible Service System (FSS) determines your next scheduled oil change based on how you drive the car. The minimum mileage the computer will let the car go between oil changes is 10,000 miles. The maximum is 20,000. Most people will get the indicator for service between every 11,000 and 13,000 miles. You can manually check to see when the next service is due by bringing up the main odometer screen, and then press the up or down arrow buttons until you get the screen that says "A service in XXXX miles" or "B service in XXXX miles". Once you get to within 1,000 miles of the next service due date, the screen will automatically pop up when you start the car.
Your display says "perform service on time" because either the car was uneven or it was just turned off and the oil had not all drained into the pan. Don't use this method to check your oil anyways, it's a shady, unreliable way to check it. I advise checking the oil level with the dipstick under the hood. The dipstick never lies. If the oil level is too low or too high, the display on the cluster will alert you, but again, this is very unreliable. Many 2000 and 2001 model cars have had faulty oil level sensors that indicate "Oil level high" when in fact the level was OK.