No, the rule you posted didn't quite say that. It said nothing about "same day/same night". Nor did it provide any guidance for, if that is the intent of the rule, when JV and varsity rosters may be changed. What if a guy started varsity Tuesday but didn't start varsity Friday? The rule you quoted says nothing at all about same day/night, which is why I believe the intent of the rule you quoted is at the other end...to be inclusive. This would not be the first area where the TSSAA handbook is vague.
On the other hand, this is from the preamble:
"At the junior varsity or B-Team level, the only eligibility rules that apply are those in Sections 1 (Enrollment), 2 through 4 (Academic Rules), 5 (High School Graduate), 6 (Eight-Semester Rule), 7 (Repeating Rule), 8 (Eighth Grade Participation), 9 (Age Limit), and 10 (Physical Examination and Parental Consent). At the varsity level, all eligibility rules apply."