Hi, Giangilberto from Milan, I'm telling you this as an Italian. I lived in NYC for almost two years, so I know your culture quite well, especially when it comes to tipping, and above all, I know my own perfectly.
My answer to your question is no.
I don't think the custom of tipping is catching on, it's not part of our history, our culture. I'll explain what's happening, from my perspective.
What's changed isn't the Italian custom: it's the terminal.
Since 2022, POS terminals have been mandatory by law, with no minimum threshold. Within two years, all restaurants have changed their machines, and the new terminals, almost all from international operators, have the tip screen activated by default.
The waiter isn't asking for it, the machine does it for them, and that's exactly why they seemed embarrassed and specified that it's not mandatory, they're subjected to that screen too.
In Italy, we already pay a cover charge, one or three euros per person on the bill, it's the historical equivalent of service, and it's the reason why tips have never been expected.
You can safely skip the screen, no one will be offended, and leaving a few coins if you're satisfied remains what it always has been a gesture, not an obligation.
The fact that the waiters were uncomfortable is proof that this isn't an Italian innovation, but a software innovation.
Some studies have shown that in Italy there's a sharp increase in tips left via POS, but I can assure you that the phenomenon is due to foreign users.
We don't do it, and if we do, we do it in cash, not via POS.