Yes, those are the right settings, as far as I know (I'm quite far from Italy).
And there is no reason -- in terms of AquaMail -- why this should not work.
And I understand that it does when the phone is connected to WiFi.
There is nothing different in AquaMail for WiFi vs. mobile data -- so the actual difference is your mobile provider.
The only thing I can think of -- please check AquaMail settings -> network and make sure that the one that mentions "DNS" (second from the top) is *enabled*. But then it is enabled by default.
I'd maybe try an app like K9 Mail as a "sanity check"...
Oh and I'd also try these server names instead:
in.aliceposta.it and out.aliceposta.it (instead of *.alice.it), here is why:
$ dig in.alice.it
;; ANSWER SECTION:
in.alice.it. 4857 IN CNAME in.aliceposta.it.
in.aliceposta.it. 3367 IN A 82.57.200.129
$ dig out.alice.it
;; ANSWER SECTION:
out.alice.it. 86245 IN CNAME out.aliceposta.it.
out.aliceposta.it. 3445 IN A 82.57.200.132
Some phones / networks have trouble resolving DNS names when there is a CNAME redirection in the middle.