Your teen is happy because he has completed his Common Application main essay and all the questions. He may think he is done writing. Not likely. More essays, just as long as the Common Application main essay, can be lurking in the supplements for each college on his list.
Encourage your teen to look carefully at the supplements before doing a victory dance. Getting them done now will mean that he won't have to deal with them later when his homework and test schedule will be full.
Keep in mind that some colleges are already accepting applications and that your teen should carefully plan his application submission strategy for best admission and scholarship results.