Sorry,I never heard the term of 'tax month'.
Based on what I know, your 2008 income will be taxed in 2009.
If you stay more than 183 days in singapore in 2008, you will be taxed as a resident. But if you stayed less than 183 days in singapore, you maybe taxed at 15%(or resident rate depends on which one is higher). But if you can prove to the authority you have left singapore for certain reason(i.e, send overseas to do projects by your company), you may still be taxed as a resient.
But frankly saying, normally IRAS won't do such detailed checking to individuals.
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