Recently, experiments reported a strong memory effect of crystallization in model ethylene-based homogeneous random copolymers after being annealed at temperatures higher than the equilibrium melting point of copolymers. By means of dynamic Monte Carlo simulations of random copolymers, we reproduced this phenomenon in the similar model copolymer systems. We attributed this phenomenon to the sequence-length segregation upon first-time crystallization. The resulting heterogeneous melt of copolymers survives upon annealing below the critical demixing point that could be much higher than the equilibrium melting point of copolymers. Therefore, the local high concentration of long sequences raises the local melting point to accelerate primary crystal nucleation upon second-time crystallization. This source of memory effects demonstrates how crystallization can be influenced by the substantial trend of demixing between different sequences in homogeneous random copolymers.