According to the Neumann boundary condition, we consider some family of nonlocal operators related to reflected stochastic differential equations driven by multiplicative isotropic α-stable L'evy noise (1 < α < 2) in a domain D ⊂ Rd. We study by using homogenization theory the behavior of uε,δ: D -→ R of semilinear partial differential equations with periodic coefficients varying over length scale δ and nonlinear reaction term of scale 1/ε. The behavior is required as ε, δ both tend to 0. Our homogenization method is entirely probabilistic. Since δ decreases faster than ε, we may apply the large deviations principle with homogenized coefficients. [ABSTRACT FROM AUTHOR]