Yeah, you are gonna be taxed for it. As others have said the cost that Republic covers is compensation that doesn't fall under regular employment. Therefore, you will be issued a 1099 as you would for any kind of miscellaneous compensation of a large amount that you received from anywhere.
Apparently you haven't done many self-employment related tax returns in the past or this would not be a surprise to you. Nonetheless, since you are surprised you should also be aware that this is standard tax withholding procedure considering you are not yet an employee while taking the ATP-CTP.
A fix that could prevent that from happening is to make the new hires actual employees on their ATP-CTP start date. One possible reason this has not happened is that it would screw over the guys who already have their ATP (i.e., current 121 pilots) who would be junior to the ATP-CTP students in their indoc class.