I finally found the solution.Someone here actually said that the ConvertScene() doesn't affect the vertices array but sets node global/local matrices.With these we can then transform the node geometry or the vertices.
So here how it is done:
FbxMatrix globalTransform = mesh->GetNode()->GetScene()->GetEvaluator()->GetNodeGlobalTransform( mesh->GetNode());
dvec4 c0 = glm::make_vec4((double*) globalTransform.GetColumn(0).Buffer());
dvec4 c1 = glm::make_vec4((double*) globalTransform.GetColumn(1).Buffer());
dvec4 c2 = glm::make_vec4((double*) globalTransform.GetColumn(2).Buffer());
dvec4 c3 = glm::make_vec4((double*) globalTransform.GetColumn(3).Buffer());
glm::mat4 convertMatr =mat4(c0,c1,c2,c3);
convertMatr = inverse(convertMatr); //need to inverse otherwise the model is upside down
Then use convertMatr to transform mesh's vertices.Hope it will be helpful to anyone as Autodesk forum is not too much responsive.