Yes, on your 2018 tax return you can claim a credit for tuition that you paid in 2018 for classes that start within the first three months of 2019. The payment will be included in your 1098-T, if the school fills out the 1098-T correctly. The 1098-T is supposed to include all the payments they received in 2018, including payments for the spring 2019 semester. I wouldn't say that it will be included "automatically." It depends on the school doing it right.
