Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) inhomogeneous superconducting (SC) state, first- and second-order phase transitions, and quantum criticality induced by spin accumulation in a ferromagnet-$d_{x^2-y^2}$-wave superconductor-ferromagnet tunnel junction are theoretically predicted. A complex phase diagram in the temperature-bias voltage plane is determined. It is found that the phase transitions from the homogeneous BCS state to the inhomogeneous FFLO state, and from the FFLO state with the momentum $q$’s azimuthal angle ${\theta }_q=0$ to that with ${\theta }_q=\pi /4$, are of the first order, whereas the transitions from all SC states to the normal state at critical voltages are of the second order. A Lifshitz point, a bicritical point, and a quantum critical point are identified.