We analyse a posteriori error estimates for the discretization of the neutron diffusion equations with a Domain Decomposition Method, the so-called DD+$L^2$ jumps method. We provide guaranteed and locally efficient estimators on a base block equation, the one-group neutron diffusion equation. Classically, one introduces a Lagrange multiplier to account for the jumps on the interface. This Lagrange multiplier is used for the reconstruction of the physical variables. Remarkably, no reconstruction of the Lagrange multiplier is needed to achieve the optimal a posteriori estimates.