I think one can use Yod, Aleph, Waw and He to indicate vowels in Hebrew (and presumably Phoenician) when it isn't obvious. Hence why the Greeks turned them into Iota, Alpha, Ypsilon and Eta.
Close. Phoenician & Aramaic (which is just a name for the form that Phoenician letters had evolved into in a later era) only did the dual-use thing with three letters: waw/wau, yod/yud, and ʔalif/ʔaleph. These equate to modern standard Greek upsilon, iota, and alpha. I don't think the Phoenicians were using them that way yet when the Greeks made full-time vowels out of them, but users of the Phoenician/Aramaic alphabet would make the same associations later. Either way, though, those three were it for the Semitic languages.
The Greeks still had three or four more vowel sounds that those don't account for, and based their symbols for them on letters which the Phoenician alphabet retained as consonants. One of those was ʕayn, on which the Greeks based their letters for two sounds that would be lumped together as "o" in most languages: a "big" one and a "little" one, O-mega and O-micron.
The history of the remaining two letters was made a bit messy by the fact that not all Greek dialects agreed on whether "h" counts as a distinct sound or how many e-like sounds needed to be distinguished. Phoenician had two h-like sounds, which both seem to have had an e-like effect on the vowels
after them, to outsiders like the Greeks, whether that was a distinct phoneme in Phoenician or not. The lighter one, equivalent to our "h", was represented by Phoenician he, which the Greeks adopted as epsilon, which was always a vowel (and gave us our E).
The heavier or more "emphatic" one, pronounced with some constriction in the throat or back of the mouth, was represented by Phoenician ḥet. The Greeks did adopt this as the letter eta (which looks like our H), but not necessarily as a vowel at first. Some dialects used it for the sound "h", while others used it for a second e-like vowel. Eventually the latter became standard (after the Italians had gotten the alphabet from somebody who had been doing the former). With eta as a vowel, the sound "h" was treated not as an independent sound but as a way of breathing for vowels and "r"s, indicated by only a diacritical mark called a "dasia" above the affected real letter. In Phoenician it simply remained nothing but a consonant, never used as a vowel.
All of that about the Greek alphabet happened long before anybody speaking any Semitic language ever thought of using either he or ḥet as a vowel, and before the ancestor of any modern Semitic language even
had a vowel sound like "e" to represent with it, with no input from or effect on any contemporary Semitic language.
All modern Semitic alphabets are descended from the Aramaic one, so they all inherited the dual uses for the three letters I named above, and no more. But Hebrew later evolved to have not three but five vowel sounds. One letter, the original waw/wau, thus ended up as a consonant (which has shifted from "w" to "v" so now the letter's name is "vav") and
two distinct vowels: both "u" and "o". The other new vowel sound, "e", wasn't around when the Greeks were deciding what to do with their epsilon and eta. Now that it is here, it's perceived as sounding like it's somewhere between the sounds "a" and "i", and it may have evolved from both in different settings, so it's inconsistently represented by either alef, yod, or a new fourth part-time vowel letter, he... which is the evolutionary equivalent of epsilon, but was not used this way til epsilon had been around for ages.