Spontaneous self-assembly of a multication nanophase in another multication matrix phase is a promising bottom-up approach to fabricate novel, nanocomposite structures for a range of applications. In an effort to understand the mechanisms for such self-assembly, complimentary experimental and theoretical studies are reported to first understand and then control or guide the self-assembly of insulating BaZrO3 (BZO) nanodots within REBa2Cu3O7 (RE = rare earth elements including Y, REBCO) superconducting films. The strain field developed around BZO nanodots embedded in the REBCO matrix is a key driving force dictating the self-assembly of BZO nanodots along REBCO c-axis. The size selection and spatial ordering of BZO self-assembly are simulated using thermodynamic and kinetic models. The BZO self-assembly is controllable by tuning the interphase strain field. REBCO superconducting films with BZO defect arrays self-assembled to align in both vertical (REBCO c-axis) and horizontal (REBCO ab-planes) directions result in the maximized pinning and Jc performance for all field angles with smaller angular Jc anisotropy. The work has broad implications for the fabrication of controlled self-assembled nanostructures for a range of applications via strain-tuning.