For most employees each paycheck is handled in isolation. The tax calculations don't care what you made last paycheck or what you will make next paycheck. The employer doesn't know what you made or will make with other employers.
The tables in IRS pub E do the best job of explaining how your federal tax is calculated.
Based on your pay period being every two weeks each of the 2 allowances is worth $155.80. This amount does not depend on single or married, only the fact that 155.80 *26 is worth approximately 1 personal exemption ($4050 in 2016).
Therefore before determining your tax, the payroll company removes the value of the allowances as directed on page 42:
$673.08 Gross pay
$311.60 subtracts the value of two allowances
-------
$361.48 this is then used to calculate the tax to withhold.
Now moving onto the table 2 (single and biweekly pay) on page 44 they withhold $0 plus 10% of the amount over $87.
For you they should withhold (361.48-87.00)*0.10 or $27.45 (I have seen other employers round the tax withholding to the next dollar)
For the tax tables they see somebody that makes $17,500 a year and will have personal exemptions and standard deductions worth ~10,000.
The tax tables don't do a good job of withholding for people who have variable pay (too little withheld on small paychecks and too big on large paychecks), part year income (too much withheld), and multiple jobs (each is in isolation)
note: if the company pays every two weeks and that example check only covered 1 week, the next check will have the social security and medicare amount withheld double, but the federal withholding will jump to about $89 because that tax tables would treat your annual income as being in the 15% tax bracket.
