I started reading the section of NCAA bylaws (15.5.5.3) on this and there are a number of exceptions.
Here is the initial counter rule as it applies to athletes entering in winter or spring quarter.
A student-athlete recruited by the awarding institution who enters after the first term of the academic year and immediately receives institutional financial aid (based in any degree on athletics ability) shall be an initial counter for either the current academic year (if the institution's annual limit has not been reached) or the next academic year. The student-athlete shall be included in the institution's total counter limit during the academic year in which the aid was first received.
Here is another exception from a little further into the bylaws.
A counter who graduates at midyear or who graduates during the previous academic year (including summer) may be replaced by an initial counter, who shall be counted against the initial limit for the following academic year, or by a student-athlete who was an initial counter in a previous academic year and is returning to the institution after time spent on active duty in the armed services or on an official church mission. In bowl subdivision football, an institution may use the midyear replacement exception only if it previously has provided financial aid during that academic year to the maximum number of overall counters (85 total counters).
Here is a link to the section in the bylaws.
https://goomer.ncaa.org/wdbctx/LSDBi/LSDBi.LSDBiPackage.GetBylawToDisplay?p_Division=1& p_Key=8810&p_Bylaw=15.5.5.3&p_ViewAdopted=Adopted& p_TextTerms=(%60initial%20counter%60)&p_TitleTerms =ThisIsADummyPhraseThatWillNotBeDuplicated&p_HeadF oot=1&p_CallCount=1