Stacked EuTe magnetic quantum dots (QDs) separated by SnTe spacers of increasing thickness were grown and studied using x-ray diffraction (XRD) and electron microscopy. Grazing incidence XRD indicated that the EuTe QDs are under compressive in-plane strain. Both XRD analysis and microscopy images demonstrated that the EuTe QDs are vertically aligned, as a result of the strain field produced by buried QDs. The width of the lateral error distribution in the QDs' vertical alignment from layer to layer decreases for thinner SnTe spacers, corresponding to more stressed SnTe matrices. The system can be, therefore, tuned to explore magnetic interactions between QDs. The results are discussed in the light of previous elastic strain models in anisotropic matrices from the literature.