This paper proposes a general scheme based on terminal attractors to parametrize operational tasks with respect to time in continuous kinematic controllers. Commonly, a pseudo-inverse operator is applied to solve operational tasks. However, it is known that discontinuities in the control signals appear as a by-product of task transitions during motion execution. In particular, these transitions involve the insertion, removal and swapping of tasks. Recently, some methods have been reported that overcome such discontinuities in the control signals. In this work, we provide time parametrization capabilities to these continuous kinematic controllers in order to handle the time axis of operational tasks at will. Then, we show that the proposed scheme can be naturally extended for the case of prioritized kinematic tasks while preserving continuity under task transitions. Our scheme is validated in a real experiment with a NAO humanoid robot.