Should I add a second State of residence in a situation that was temporary?

The employer sent your W2 to the state already if it has state information on your W2. Making the address match the w2 is correct. Since you were there for a temporary job, you were not a resident of the state. You would be a nonresident on the tax return. You may not need to file a state return, depending on the state and the income. If you reply with the state and income amount, we are glad to tell you if it needs to be filed.

Hello Amy. 

Thank you for the explanation. 

The total income on my W2 for that job was $22,940 (1). The state that I was living was Florida but the only place that says that is on the Employee's address information (e). They didn't add any information on the State fields (15, 16 and 17). 

With these additional information do you think I need to report FL as a residence that I had and file a FL state return?     

Florida does not have a state income tax return, so you don't need to add Florida as a state you lived in. Besides, if you were there temporarily, you would not be considered to have lived in that state.