In this work, two approaches, based on the certified Reduced Basis method, have been developed for simulating the movement of nuclear reactor control rods, in time-dependent non-coercive settings featuring a 3D geometrical framework. In particular, in a first approach, a piece-wise affine transformation based on subdomains division has been implemented for modelling the movement of one control rod. In the second approach, a "staircase" strategy has been adopted for simulating the movement of all the three rods featured by the nuclear reactor chosen as case study. The neutron kinetics has been modelled according to the so-called multi-group neutron diffusion, which, in the present case, is a set of ten coupled parametrized parabolic equations (two energy groups for the neutron flux, and eight for the precursors). Both the reduced order models, developed according to the two approaches, provided a very good accuracy compared with high-fidelity results, assumed as "truth" solutions. At the same time, the computational speed-up in the Online phase, with respect to the fine "truth" finite element discretization, achievable by both the proposed approaches is at least of three orders of magnitude, allowing a real-time simulation of the rod movement and control.