Short answer. Yes, within limits. The Labor Code allows compulsory overtime where a calamity such as fire, flood, typhoon or earthquake creates an actual or impending emergency in the locality and the work is necessary to prevent loss of life or property or danger to public safety.
What the law says
When it is necessary to prevent loss of life or property or in case of imminent danger to public safety due to an actual or impending emergency in the locality caused by serious accidents, fire, flood, typhoon, earthquake, epidemic, or other disaster or calamity
Labor Code, Article 89 — Emergency Overtime Work. Read the full provision →
The calamity is not by itself the justification
The ground reads: when it is necessary to prevent loss of life or property or in case of imminent danger to public safety due to an actual or impending emergency in the locality caused by serious accidents, fire, flood, typhoon, earthquake, epidemic, or other disaster or calamity. There are two halves and both must hold. There must be an emergency in the locality caused by one of those events, and the overtime must be necessary to prevent the loss or the danger. A typhoon outside does not, on its own, make every extra hour compellable — the hours have to be doing the preventing.
"In the locality" and "impending" both do work
The emergency must be in the locality, so a calamity affecting a distant branch or a supplier does not engage this ground where you are. But it need not have arrived: an impending emergency counts, which is what allows work ahead of a storm rather than only after it. The list of causes ends with other disaster or calamity, so it is not closed to events the drafters did not name, though the added event has to be of that character — a disaster, not a bad quarter.
Your own safety is not answered by this article
This provision says when overtime may be required. It does not say that an employer may require you to travel through a flood, remain in an unsafe building, or work in conditions that endanger you, and it should not be read as an answer to those questions. Occupational safety is governed by its own body of law and by the employer's duty to provide safe working conditions. If what is being demanded is dangerous rather than merely long, the objection to make is a safety objection, and it is a different one.
It remains compensable, and the record matters
Emergency overtime is paid overtime — the same article provides for the additional compensation. Write down the dates and hours as they happen, since payroll after a calamity is frequently reconstructed from memory and yours may be the only contemporaneous account. Note what you were told the work was for. If a suspension of work was announced for your area and you were nonetheless required to report, that fact is worth recording too, and worth raising with a lawyer if pay or safety later becomes an issue.