Tax and CPF (Singapore)

Wondering if there's anyone in the same situation who can help.

I'm a Singaporean who is hired by a Malaysian agency which subcon me to a Malaysian company that posted me to its Singapore branch.

I am receiving my salary directly from my agent / Malaysian agency in Malaysia.
Technically I am working for a Malaysian company in Malaysia, I'm just on 'job trip' here in Singapore. In reality, well, I am working in Singapore full time.

So do I still have to contribute to CPF and pay the tax here in Singapore?