Often times when you receive multiple W2s, the combined income pushes you into a higher tax bracket. However, each individual W2 assumes you're in a lower tax bracket because it doesn't know about the income from other sources, and therefore under-withholds what is necessary for taxes. This is likely what is occurring in your situation.
In future years, if you expect to receive multiple W2s, you can use a free tool such as Intuit TaxCaster to help estimate what your tax liability will be, and can adjust your W4 accordingly so that it withholds to appropriate amount.