Generally this process is called prothesis when it occurs at the start of a word (epenthesis occurs between two sounds). This process did indeed involve the addition of a vowel to the start of words with these clusters.
History of the prothetic vowel insertion
From what I see here, your source only says that this happened in Vulgar Latin; it is silent on the question of whether this process occured during Old French. To find out whether this was an active process in Old French, the place to look would probably be at words that we know, from some other evidence, had to have come into the language around that time and that started with one of the sc- sp- st- clusters. If Old French writers added an "e" before words like this, we would know they still had difficulties pronouncing the cluster at the start of a word; if they took words like this into the language with the cluster unchanged, we would know that they no longer had any problem with these clusters.
The reference to Germanic words with the prothetic vowel may indicate this process continued into Old French, but you'd have to know when the Germanic words entered the language. From what's written here, it could also be the case that these Germanic words were first taken in by an earlier ancestor of both French and other Romance languages (that might be what the author means in speaking of "Romanic" loanwords). And of course, Old French was not a uniform language across all the times and places it was spoken: perhaps in earlier Old French there was still prothesis, and in later Old French it no longer occurred. It isn't logically necessary for the vowel prothesis to have still been an active process in Old French, though: once the prothetic vowels were introduced in Vulgar Latin, they were simply passed on into successive versions of French, and indeed the vowels remain in the modern descendants of these words, despite the fact that the process that created them is now obsolete.
I found a few more details about the history of prothetic e- in French in an article about prothetic e- in modern Spanish:
In 11th century old French, a prothetic vowel before #sC occurred only after a consonant (e.g., “il out espusethe” [he had married]), not after a vowel (e.g., “la spusa” [the spouse]). In 12th century old French, however, the prothetic vowel generalized, as well as in Iberian Romance languages. Later on, due to borrowings from old Latin, Germanic, and other languages, the systematicity of the prothetic vowel was lost in French, but not in languages such as Spanish.
(p. 4, "special is especial but stuto is not astuto: perception of prothetic /e/ in speech
and print by speakers of Spanish", by Pierre A. Hallé, Juan Segui, Alberto Dominguez, and Fernando Cuetos)
(Note however that in modern Spanish, the phenomenon of "synalepha" means that word-initial "e" will typically be pronounced in the same syllable as the last vowel of a preceding vowel-final word, and in modern French, the definite article la has its vowel elided before most vowel-initial words, resulting in l', so "the spouse" is "l'épouse".)
As you know, in Modern French there is no such active process of prothesis for words starting with sc- sp- st- clusters, as we can see from words like scolaire and sportif and stupide. These words were not exactly "reverted" to the Latin form just in spelling; rather, they were re-introduced, with both new Latin-based spellings and new pronunciations, by learned individuals who knew Latin, and the terms then developed to become part of the modern French language. (This class of words, which, rather than developing continuously and directly from Vulgar Latin, were re-introduced or altered on the basis of their written Latin source, are sometimes referred to by the name cultismes or cultisms.)
In general, more intellectual, fancy, rarely-used terms are more likely to have been brought closer to the Latin forms in this way, and the more common, everyday and ordinary words are more likely to have changed and diverged the most from Latin. There are many noun-adjective pairs in French where the noun has some sound changes that were reversed or resisted on the adjective: a relevant example for this particular sound change is the pair école-scolaire, where we see that the noun has the excrescent e- and has lost the s while the adjective simply has the same initial consonant cluster as the Classical Latin word.
Origin of the process
As for why the original Vulgar Latin speakers found these clusters difficult: "why" questions can be difficult to answer in linguistics, unfortunately. However, there's nothing wrong with the question in principle, and hopefully someone with a more expert knowledge of historical linguistics and of phonetics than mine will give you a good explanation. Based on what I know, it tends to be considered easier in general to pronounce clusters following what is known as the "sonority hierarchy", where at one end are the plosives, sounds that cannot be extended at all like "p" "t" "k", and at the other end are gliding and liquid sounds like "w" and "l". In initial clusters, low-sonority sounds like plosives tend to precede high-sonority sounds like glides and liquids, so it is easier to pronounce a syllable like "pla" than it is to pronounce one like "lpa".
Fricative sounds like "s" or "f" are generally considered to lie in between these two types of sound in sonority. So by this theory, we should expect the most natural clusters with "s" to be clusters like "sla" and "psa"; a consonant cluster like that in "spa" has the sounds "the wrong way around" in terms of the sonority hierarchy; the cluster is to some degree an exception to the general principle, which might explain why it was made easier to pronounce by inserting a vowel before it in Vulgar Latin.
It may be relevant that in Classical Latin, even though sc-, sp-, st- were tolerated as clusters word-initially, they seem to have typically been syllabified as -s.c-, -s.p-, -s.t- in word-internal intervocalic contexts, judging by the operation of the Classical Latin stress rule which is sensitive to syllable weight.