Two different sets of rules/ministries in play here (three actually, if you consider ICA as well as you will be transiting through Immigration.
While I cannot find the black & white (I haven't looked as of yet), I believe that you will not pay any income taxes to Singapore even though you receive your money here (Singapore only taxes income that is actually earn IN SINGAPORE). As you are being hired by a Singapore Employer and are on a temporary assignment in Korea, you can still keep your EP as/when the position is finished in Korea, supposedly you will return to work in the Singapore Office.
If you are being paid on a monthly basis, then your income would necessarily have to be prorated between your time in Korea and your time in Singapore (even though you are off in theory but are still employed by the Singapore employer) Bit different if you are on a day rate. Actually, They could have hired you on a offshore contract (signed while you were on the plane to Korea and sent back via courier when you land, and you could have just come to Singapore on a bog stand SVP after every 3 month hitch. That what I did here for the first 11 years in Singapore. I work a 2 month on/one month off rotation (on month off on a SVP in Singapore. The first year I lived in the company's staff house and then I got married to a local so had my own lodging (albeit in her name). I did that for 11 years before taking up a position in Singapore and getting an EP.
The look on the ICA Officer, who gave me my PR interview, was a MasterCard moment when I told him I'd had one Singapore wife, 2 Singaporean children and three Singapore registered cars (and a C & D license) all on Standard 30 day SVPs spanning 11 years. I thought his jaw was going to hit the floor. Never paid any taxes. Never filed a Singapore tax return as I was only a tourist here.
