Besides epitaxial mismatch that can be accommodated by lattice distortions and/or octahedral rotations, ferroelectric-ferromagnetic interfaces are affected by symmetry mismatch and subsequent magnetic ordering. Here, we have investigated La0.67 Sr0.33 MnO3 (LSMO) samples with varying underlying unit cells (uc) of BaTiO3 (BTO) layer on (001) and (110) oriented substrates in order to elucidate the role of symmetry mismatch. Lattice mismatch for 3 uc of BTO and symmetry mismatch for 10 uc of BTO, both associated with local MnO6 octahedral distortions of the (001) LSMO within the first few uc, are revealed by scanning transmission electron microscopy. Interestingly, we find exchange bias along the in-plane / directions only for the (001) oriented samples. Polarized neutron reflectivity measurements confirm the existence of a layer with zero net moment only within (001) oriented samples. First principle density functional calculations show that even though the bulk ground state of LSMO is ferromagnetic, a large lattice constant together with an excess of La can stabilize an antiferromagnetic LaMnO3-type phase at the interface region and explain the experimentally observed exchange bias. Atomic scale tuning of MnO6 octahedra can thus be made possible via symmetry mismatch at heteroepitaxial interfaces. This aspect can act as a vital parameter for structure-driven control of physical properties.