as pointed out by @miniR, it is not necessary.
Timestamp ordering protocol requires the schedule to be conflict serializable in the order of the increasing timestamps. For example,
Let TS(T1) = 10, TS(T2) = 20; If the schedule turns out to be conflict serializable in the order T2->T1, it still does not get accepted in the timestamp protocol, and T1 gets aborted and re-enters the system with a new timestamp.