hello, you are welcome, I am just glad I can help from my own experience.
You don't need to that pay tax at 15% rate
1. if you don't quit your 2nd job before the end of financise year, which is in the end of Dec this year
or
2. your working days for this 2nd job along with working days from this 1st job is more than 183 days in the same year, eg 2005.
I have been to their taxation office, was advised face to face, IRAS only counts actual your employed days tho.
And, as long as you work up to exact 183days, then you are safe in anyway.
Have you actually looked into this website ? If haven't, here it is again.
http://www.iras.gov.sg/ESVPortal/Home/index.asp
Be aware that your scenario could repeat in every calendar unless your status changes to PR or something.