JuMP does not reformulate max.
model = Model()
@variable(model, x[1:2])
@objective(model, Min, max(x[1], x[2]))
becomes
model = Model()
@variable(model, x[1:2])
@variable(model, z)
@constraint(model, [i=1:2], z >= x[i])
@objective(model, Min, z)