Residency status for fy2012-13

I have a query on Residency status. I had travelled to the US on Oct 27, 2011 and returned to India on Nov 30, 2012. My company has listed me a US resident (since I was in the US from Jan to Dec 2012) and also as an Indian resident due to the Rule (b) below:

1. An associate is in India for 182 days or more during the current financial year
   
   OR
   
   b. An associate is in India for 60 days or more in the current financial year and for 365 days or more in the preceding four financial years

Due to this, I had to pay Income Tax in both the US and in India. Can someone clarify how I can be a resident of two countries in the same year? Is this because of the fact that the Financial Year is treated differently in the US (Jan-Dec) and India (Apr-Mar)?

Please help me understand this. Is there a way I can get a refund of the tax that I've paid in India? Thanks in advance