I don't have direct experience of the US tax and education systems, but it appears (e.g. from Form 1098-T on Wikipedia) that (at least part of) the purpose of From 1098-T is to record certain tuition and educational expenses paid by a student out of their own pocket. These records can then potentially be used to claim The American Opportunity Tax Credit (introduced in 2009, replacing earlier schemes).
The IRS page About Form 1098-T, Tuition Statement contains links to Instructions for Forms 1098-E and 1098-T in either PDF or HTML format. From those instructions (some highlighting mine):
Specific Instructions for Form 1098-T
File Form 1098-T, Tuition Statement, if you are an eligible educational institution. You must file for each student you enroll and for whom a reportable transaction is made. Also, if you are an insurer, file Form 1098-T for each individual to whom you made reimbursements or refunds of qualified tuition and related expenses.
Exceptions. You do not have to file Form 1098-T or furnish a statement for:
- Courses for which no academic credit is offered, even if the student is otherwise enrolled in a degree program;
- Nonresident alien students, unless requested by the student;
- Students whose qualified tuition and related expenses are entirely waived or paid entirely with scholarships; and
- Students for whom you do not maintain a separate financial account and whose qualified tuition and related expenses are covered by a formal billing arrangement between an institution and the student’s employer or a governmental entity, such as the Department of Veterans Affairs or the Department of Defense.
If your tuition is "automatically taken from financial aid", then it seems to me that the highlighted bullet-point would apply, and the college is not required to file a Form 1098-T. Since you have not paid these expenses out of your own pocket, I presume you are not able to claim The American Opportunity Tax Credit on those fees, and so no 1089-T is needed.
Financial Aid Checks
From your description, it appears that you are receiving some form of financial aid. This covers your tuition fees, and whatever is "left over" is sent to you as a check. You are concerned "that I don't get in trouble with the IRS".
It may well be that you have some obligation to report the "left over amounts" (or, indeed, the whole amount). On the other hand, it may not need reporting, or may already be being reported. What seems fairly certain is that whatever reporting requirements that might exist are not related to From 1089-T.
If you are concerned about a possible need to report all or part of the financial aid, I would suggest asking a separate question, giving details of the source of the financial aid.