Welcome back to the Wefugees Community and thank you for your question!
This platform and our experts are based in Germany. Therefore, I am afraid that we are unfortunately not able to share too much details or experiences on procedures and regulations in Italy. I tried to make some research and found this website which gives some good information on family reunification in Italy. I also read here that in general recognized refugees and people under international protection enjoy a privileged right for family reunification and are not asked to provide a proof of income or accomodation. However, in Germany for instance, people need to "register" their wish to reunite with familiy members within a certain period after they received the formal status as refugee. If they don't let the authorities know about their plans to bring family members, they might have lost their privilege and need to provide those kind of proofs of being able to take care about the respective persons. On the the website I refered to, experts are offering to answer indiviudal questions, via Facebook for example. I would highly recommend you to get some local support or consulting on the details and further questions.
I hope this helps and all the best,