I have tested the new version NLPModels v0.13.2. It indeed reduces the number of evaluations to half!
In a final summary, for the same tolerance of the gradients (g_tol and outer_g_tol = 1e-4 for Optim.jl and atol = 1e-4 for JSOSolvers), to optimize my problem, JSOSolvers requires 12 evaluations and Optim.jl requires 24 evaluations.