Short answer. Yes, they still have to pay it. Labor Code Article 88 says permission to take a day off on another day does not exempt the employer from paying the extra compensation the law requires for overtime work. A compensatory day off can be given on top of the overtime pay, but it cannot replace the overtime premium.
What the law says
Permission given to the employee to go on leave on some other day of the week shall not exempt the employer from paying the additional compensation required in this Chapter
Labor Code, Article 88 — Undertime Not Offset By Overtime. Read the full provision →
What the law says
Undertime work on any particular day shall not be offset by overtime work on any other day
Labor Code, Article 88 — Undertime Not Offset By Overtime. Read the full provision →
A day off is not a substitute for the premium
Article 88 addresses a common arrangement: an employer lets an employee take a day off instead of paying for overtime already worked. The law is explicit that this kind of permission does not excuse the employer from paying the additional compensation the Labor Code requires for overtime. Whether the day off is called a rest day, a compensatory day off, or simply time off in lieu of pay, it does not substitute for the premium itself. The overtime premium is a statutory entitlement tied to hours actually worked beyond the normal schedule, and it is paid in money, not offset in time.
Undertime and overtime cannot be netted against each other either
The same article also blocks a related shortcut: an employer cannot net out undertime on one day against overtime on another. If an employee arrives late or leaves early on Monday and then works late on Wednesday, the employer cannot treat the Wednesday overtime as merely canceling out the Monday shortfall. Each day's hours are counted on their own terms — undertime is deducted from pay for that day, and overtime is compensated for that day, without cancelling each other out across the workweek. This prevents employers from quietly absorbing overtime pay obligations by pointing to unrelated shortfalls on other days.
What this means if your employer offers a trade-off
If your employer offers you a day off in exchange for overtime you already worked, you can generally accept the day off, but that offer does not by itself settle the overtime pay owed to you. The employer still has to pay the overtime premium for the hours actually worked beyond the normal schedule, on top of whatever schedule accommodation is given. If your payslips show overtime hours worked but no corresponding overtime pay, and the explanation given is that you were allowed to take time off instead, that arrangement does not satisfy the employer's obligation under this article.