This if from the IRS, and it seems vague because of the word "may".  I don't know what triggers the word "will". If your client earns money throughout the year, I would recommend to them that they make the four payments throughout the year rather than one at the end. 

When to pay estimated taxes

For estimated tax purposes, the year is divided into four payment periods. Each period has a specific payment due date. If you don’t pay enough tax by the due date of each of the payment periods, you may be charged a penalty even if you are due a refund when you file your income tax return.

https://www.irs.gov/businesses/small-businesses-self-employed/estimated-taxes