I don't quite understand your question.
You are responsible for 6.2% social security and 1.45% medicare tax. If that wasn't taken out, it is absolutely a tax you owe and the employer must withhold it from your pay so that you have paid the correct amount by the end of the year. And it doesn't come back as a refund, that is your tax you owe.
If the employer withheld too much or too little state or federal income tax, that gets worked out on your tax returns at the end of the year. If the employer withheld too little at the beginning of the year, and then fixed their issue and started withholding the normal amount, it is more or less optional if they want to over-withhold to catch up. If they under-withheld, you might owe tax and a penalty when you file your return. If they over-withhold, you get any extra back as part of your tax refund.
