The understanding of size effects in micro-crystal plasticity has been in-part based on controlled uniaxial mechanical testing of crystalline micropillars that may be monitored in-situ, using modern microscopy approaches. Nevertheless, it has always been clear that mechanics and materials science are not ideally decoupled in uniaxial micropillar compression, thus agreement between experiments and theory remains challenging. We present a theoretical analysis of the uniaxial compression of micropillars with curved top free surfaces, in consistency with modern experimental thresholds. By using coupled Finite Element and Discrete Dislocation Dynamics simulations we investigate the effect of the small curvature to dislocation microstructure evolution at constant displacement rate. The uniaxial compression of flat micropillars is shown to be consistent with existing literature, with homogeneous stress build up and random activation of sources inside the volume. However, in the presence of a small top-surface micropillar curvature, there are significant dynamical effects on dislocation mechanisms and an overestimate of strain at yielding that leads to large errors on capturing elastic compression moduli and avalanche noise characteristics. Characteristically, for 10 nm-high isotropic curvature, large (>100MPa) stress drops emerge in the average stress, that become larger as the initial dislocation density increases, in direct contrast to expectations and findings for ideally flat micropillars.