Sounds like you’re referring to a fixed derate take off (TO1 / TO2) instead of an assumed temperature thrust reduction.
With a fixed derate you can use a lower VMCA which perversely in some situations can allow you to lift more, but in the case of an engine failure limits the amount of thrust you can apply on the remaining engine due to the lower airflow over the rudder. To avoid a potential loss of control if an engine fails the application of thrust greater than the fixed derate is prohibited until you’re going fast enough that VMCA isn’t an issue. It has nothing to do with time limits for various thrust settings.
Some operators have approval to use fixed derate and assumed temperature at the same time which means the thrust limit applies.
I hope that makes sense?