Microtubules and motor proteins form active filament networks that are critical for a variety of functions in living cells. Network topology and dynamics are the result of a self-organisation process that takes place within the boundaries of the cell. Previous biochemical in vitro studies with biomimetic systems consisting of purified motors and microtubules have demonstrated that confinement has an important effect on the outcome of the self-organisation process. However, the pathway of motor/microtubule self-organisation under confinement and its effects on network morphology are still poorly understood. Here, we have investigated how minus-end directed microtubule cross-linking kinesins organise microtubules inside polymer-stabilised microfluidic droplets of well-controlled size. We find that confinement can impose a novel pathway of microtubule aster formation proceeding via the constriction of an initially spherical motor/microtubule network. This mechanism illustrates the close relationship between confinement, network contraction, and aster formation. The spherical constriction pathway robustly produces single, well-centred asters with remarkable reproducibility across thousands of droplets. These results show that the additional constraint of well-defined confinement can improve the robustness of active network self-organisation, providing insight into the design principles of self-organising active networks in micro-scale confinement.