I read that Darius claimed to be very firm in his faith in Aser.

Is this an autocorrect mistake? Aser (or Asher) was one of the twelve tribes of Israel, if I'm not mistaken; do you mean "Ahuramazda"?

See below, it should be Asha/Arta, Truth, which is more of an abstract concept.

Anyway, there are layers to be uncovered here. I'm more familiar with the (sparse) Persian sources and Zoroastrianism than the Greek ones, so a Hellenist may have things to add to what I'm about to say.

First, it's important to understand, when reading Herodotus, that he's presenting a narrative of generational decay, beginning with the great Cyrus, and ending with the villainous, temple-destroying Xerxes, and therefore we cannot always take him at face value. This poses a problem, since this leaves us with fairly little in regard to Cyrus. We have the Cyrus Cylinder, which may be of interest since it recounts various Babylonian gods. However, this shouldn't be taken as an expression of Cyrus' personal beliefs, as such cylinders were extremely formal and ritual affairs that were instruments in his assertion of hegemony over Babylon.

Similarly for the Bible, we can't take at face value that Cyrus actually credited the God of Israel. The biblical portions featuring him (like Isaiah 45) are also some of the earliest assertions of monotheism in the Bible, and a very old controversy is to what extent Zoroastrianism (which features a supreme being in the form of Ahura Mazda) influenced the Hebrew shift toward monotheism. Case in point, take this bit from Isaiah 45:12 and 18:

[narrated by Yahweh] I made the earth. I created human beings to live there. My own hands spread out the heavens. I put all the stars in their places. ... Yahweh created the heavens. He is God. He formed the earth and made it. He set it firmly in place. He didn’t create it to be empty. Instead, he formed it for people to live on.

Compare to the invocation at the beginning of the XPh inscription:

A great god is Ahuramazda, who created this earth, who created yonder sky, who created man, who created happiness for man, who made Xerxes king, one king of many, one lord of many.

There is at minimum a passing resemblance between the earth-heaven-man invocation. However, there are not the mind-numbingly repetative strong assertions of the one-ness of God in Zoroastrian sources, in general. Regardless, the point here is that whatever exactly went on between Cyrus and Israel, it is plausible that they could have understood Ahuramazda as identical to the God of Israel, whether or not Zoroastrianism influenced the monotheism of early Judaism. It is also plausible that Cyrus might simply have included mention of the God of Israel as a purely political move, judging by the Cyrus Cylinder. So, unfortunately, this just doesn't tell us very much.

It's a bit easier when we get to Darius, since the Behistun inscription he comissioned is a very extensive source as far as Achaemenid kings go. Darius is pretty blunt about it:

(5) King Darius says: By the grace of Ahuramazda am I king; Ahuramazda has granted me the kingdom. (6) King Darius says: These are the countries which are subject unto me, and by the grace of Ahuramazda I became king of them: Persia, Elam, Babylonia, Assyria, Arabia, Egypt, the countries by the Sea, Lydia, the Greeks, Media, Armenia, Cappadocia, Parthia, Drangiana, Aria, Chorasmia, Bactria, Sogdia, Gandara, Scythia, Sattagydia, Arachosia and Maka; twenty-three lands in all.

He also kindly informs us of the purpose of this inscription:

(60) King Darius says: Now let what has been done by me convince you. For the sake of the people, do not conceal it. If you do not conceal this edict but if you publish it to the world, then may Ahuramazda be your friend, may your family be numerous, and may you live long. (61) King Darius says: If you conceal this edict and do not publish it to the world, may Ahuramazda slay you and may your house cease.

And even lets us know what he thinks about people who don't worship Ahuramazda (doomed to servitude?):

(72) King Darius says: Those Elamites were faithless and Ahuramazda was not worshipped by them. I worshipped Ahuramazda; by the grace of Ahuramazda I did unto them according to my will.

So, what would they gain by supporting foreign faiths? Well, for one, stability. Religion and cultural identity were and are strongly intertwined, and it's not something easily changed. More often, it's more convenient to have people go along with their ways as long as they pay tribute. Second, Zoroastrianism was and is to a strong extent an ethno-religion; it was the religion of the Aryans, who were not very interested in spreading it (this is more or less the norm with ancient religions). We can get a hint of how this may have been useful to them in the last bit I quoted: it served as an excuse for exercising sovereignty over these people and elevating one's own to a privileged class. Since Achaemenid Great Kings claimed to have been elevated by Ahuramazda, maintaining exclusivity limited the pool of people who could potentially challenge their claim to kingship. While their inscriptions do implore people to worship Ahuramazda, their are located in the Persian heartlands, and thus had a limited audience.

It is frustrating that we don't have better sources on what Cyrus actually thought, though. We can't take for granted that his beliefs were the same as those of Darius or Xerxes.