When information keeps coming in dribs and drabs, it is difficult to keep track without going back and forth. So, let me try and summarize your problem before trying to find a solution.
Current Situation Overview
You work for a company that has its HQ in Singapore. The normal working hours are 9 am till 6 pm. There are 5 departmental managers (HR Manager, Purchasing & Logistics Manager, Sales & Marketing Manager, Technical/Operations Manager, and Finance Manager) who habitually come late (between 9 am and 10 am). They stay behind till 10 pm. Workers do get paid overtime, and they do work late. However, managers are not paid overtime money. Your Principal office has asked you to give your proposal to ensure that managers come on time to work, irrespective of whether they work more than 8 hours and stay late.
Questions for Clarification
Let me ask a few more questions to get a clear picture of the problem. What is your role, as you say even the HR Manager comes late? You say that managers give unpredictable traffic as the reason for their late coming? Have you asked them if that does not apply to their workers, who come on time? Or do the workers also come late? If so, what actions do you take?
Finally, if managers are staying late every day, they can plan for their following day's work, leave instructions, and go so that even if they do not turn up for work (for whatever reason), the work will go on.