Strictly speaking:
The employer will be obliged to operate payroll deductions on it in the period when the payment is made - so they will tax the pay in January 2013.
In practise this doesn't happen and would be near impossible to implement.
People receiving paycheck on say 4th Jan 2013 are being paid for the week ending 30th Dec. The payroll system will still be in 2012 mode when that week is being processed on say 2nd Jan.