The deposit insurance isn't provided by the bank; it's provided by the Singapore Deposit Insurance Corporation (SDIC). In the event that the bank fails or is declared insolvent, the SDIC will pay deposit holders their total balance in all accounts with that bank, up to S$50,000. If you hold S$60,000 in all of your insured accounts, you'll only receive S$50,000 if the bank fails.
The SDIC provides an example page with sample calculations, and this is exactly what they show. If you deposit an amount greater than $S50,000, it's only insured up to S$50,000.
So does it mean one should open multiple accounts under different banks to spread the money around and maintain only S$50,000 in one deposit account?
This is one option. The calculations page I linked to above gives this reminder:
Deposits are not insured separately in each branch office of a DI Scheme member i.e. all your eligible accounts maintained with different branches of a DI Scheme member are aggregated and insured up to S$50,000.
This seems like common sense, but it's important to remember that if you open an account with two branch offices of Bank A, your deposits are aggregated and insured up to S$50,000. The SDIC insurance is per institution (called a Deposit Insurance Member), not per branch. If you hold S$45,000 in each branch office, for a total of S$90,000, you're still only insured up to S$50,000 for that bank. If you want to spread out your accounts between multiple banks, make sure they're different banks, not just different branches.
Another option, if it applies to you, is to open a joint account with your spouse. In the FAQ page, the SDIC gives this example under point 14:
if you and your husband have a joint account with S$70,000, and you have a separate account of S$20,000, your total deposits of S$55,000 will be covered to the maximum of S$50,000.
The deposit of $S70,000 is split evenly between the spouses, so in the eyes of the SDIC, each are holding S$35,000. Then, the husband's additional S$20,000 is added to S$35,000 for a total of S$50,000. This is then insured up to S$50,000 as usual.
I'm sure there are other options specific to Singapore that I'm not aware of; if you're well above the limit, i.e. holding millions of dollars, I'm sure a professional accountant in Singapore could guide you further.