if you work and stay more than 182 (or 190?) days inside Malaysia, then you need to pay M'sia tax, especially if SG company pays you via TT in MYR.

if SG pays you in SGD into SG bank account, then you may need to check your employment contract if you need to pay tax in SG or in MY, but not both. MY & SG has double-tax-agreement. If your SG co says you no need pay tax in SG, then you will need to declare/pay in MY.

Go do your own self contribution for both employee and employer (11 + 13%) , then submit claim for next month for the employer portion. Unless you are contract based, otherwise do not be stupid and not claim the local benefits. PCB is up to you, else have to pay lump sum duing tax filing.

That is just one of the criteria. If your income is generated in Malaysia, you still need to pay tax.
e.g. If Robert Kuok stays full time in HK, but has a company generating income in Malaysia, with his name as the director and getting income, do you think based on this rule he needs to pay Malaysia tax for that part ?

Disclaimer: It has been some time and rules may have changed now.

I'm hired as permanent employee (not contractor) directly from overseas with a letter I'm paid in MYR equivalent and the company TT into my back account. The company also agreed to follow local laws then, hence I'm entitled to submit and claim back the employer portion of EPF.
I understand in recent years, this is no longer allowed or is illegal.

Submit what claims ? I submitted a lot of claims every month then:
1) Claim back the EPF employer portion I pay. e.g. I self-contribute 1100+1300 = 2400. I claim back 1300 the next month.
2) Claim back the TT forex loses. When it is 5-digits, the forex loses can be tens/hundreds.
3) expenses/meals
4) foreign flight+accomodation
5) local travel/mileage+accomodation
6) benefits.

For what reason ? If I don't do it, I would lose out on the employer portion every month.

I fill up BE at that time as it is not a business.