Meaning of attic faith

The term Attic faith certainly seems to be rare, but not new. Ngram records 0 instances, but online sources attest to a definition in Webster's 1913 dictionary:

inviolable faith

This same dictionary also lists several related terms, and references them in its adjectival definition of Attic, which was new to me:

a. 1. Of or pertaining to Attica, in Greece, or to Athens, its principal city; marked by such qualities as were characteristic of the Athenians; classical; refined.

Attic base (Arch.) a peculiar form of molded base for a column or pilaster, described by Vitruvius, applied under the Roman Empire to the Ionic and Corinthian and "Roman Doric" orders, and imitated by the architects of the Renaissance.

Attic faith inviolable faith.

Attic purity special purity of language.

Attic salt a poignant, delicate wit, peculiar to the Athenians.

Attic story See Attic, n.

Attic style a style pure and elegant.

You go on to say,

I would like to know if it is a real phrase and its meaning is such.

It apparently is a "real phrase", in the sense that multiple authorities attest to it. I personally attribute more authority to Webster's than to the sources you listed, but any way around, multiple attestations are strong evidence. On the other hand, if by "real phrase" you mean do people actually say or write that phrase in modern English, then no. I never saw or heard it before today.

It is the case that the Wiktionary entry for Attic faith shows "Inviolable faith".

But note the capital letter. In that entry, the word Attic is also a link:

Etymology
From Ancient Greek Ἀττικός ‎(Attikós, “related to Athens”).

Adjective
Attic ‎(comparative more Attic, superlative most Attic)

1. Relating to Athenian culture or architecture.
2. Marked by the qualities that were characteristic of the Athenians; classical; refined.
3. Relating to that dialect of Ancient Greek.

Perhaps the ancient Athenian culture was noted for unshakeable faith.

You may find the entry from the OED helpful. Note that Attic is a reference to Attica or its capital Athens:

2. Having characteristics peculiarly Athenian; hence, of literary style, etc.: Marked by simple and refined elegance, pure, classical. Attic salt or Attic wit (Latin sal Atticum): refined, delicate, poignant wit. Attic faith: inviolable faith.

1633 Battle of Lutzen in Harl. Misc. (Malh.) IV. 185 Written in a stile so attick..that it may well be called the French Tacitus.

1738 Pope Epil. to Satires ii. 7 While Roman Spirit charms, and Attic Wit.

1762 L. Sterne Life Tristram Shandy V. iii. 27 Triumph swam in my father's eyes, at the repartee—the Attic salt brought water into them.

1830 T. Hamilton Cyril Thornton (1845) 49 The true attic pronunciation inculcated in Mrs. Blenkinsop's academy.

1864 M. Arnold in Cornhill Mag. Aug. 164 Well, but Addison's prose is Attic prose.

I found it used here in a footnote in an edition of The Satires of Persius and Juvenal:

for at one time 'Attic faith' was proverbially as good as 'Punic faith' was bad.

I guess the footnote is referring to this phrase of the text:

... nondum Graecis jurare paratis per caput alterius ...

... which I think implies that "faith" in this context means 'can be relied upon to keep their promises', rather than 'religious belief' (see also The Roman Concept of 'FIDES').

IMO it's so uncommon that it's no longer a "real phrase, commonly used". Even though I had some (slight) acquaintance with Classics I didn't understand that phrase (and I didn't recall having heard or read it before) when you presented it out of context.