>Once I make over a certain amount, they will start withholding federal taxes?

No. Withholdings are spread out evenly over the year. If they aren't taking any out now, they won't be taking any out unless you change your W-4 or get a big raise. $14 per hour full time is less than $30k a year. Someone making $30k per year with two kids doesn't pay federal income tax. So nothing is withheld for it.

A single person making $30k a year with no kids does pay income tax, which is why there were withholdings from your previous job.