First, Tarone has two publications from that year, so it would help to specify which one. Second, it will help you to know that she is working in a specific sub-field of second language learning theory, not general phonology. There is a general notion of "universal" used in phonology, and much controversy over how much is universal, as opposed to learned. That notion could in principle be applied to second language acquisition, and I suspect that Tarone does do so, but let's leave that aside.
In phonology, you will find some people saying that a specific phenomenon is directly built in as a universal part of the language faculty, and you will find others who say that what is universal is something more abstract (such as a theory of rule formulation) whereby various kinds of rules are "universally possible". David Stampe is an exemplar of the "actual process" view of universals, and most generative phonologists are proponents of the "abstract potential" view. There is a third view that there is no such a thing as a "universal", that humans have no specific abilities for language, instead we learn language because we can learn.
Since not all languages actually have epenthesis, both of the theories that have universals have to have some mechanism for saying that universals are not literally "attested in every language". In the generative "tool potential" view, what is made available universally is a way to say e.g. "insert a consonant in such-and-such environment", which combined with language facts would lead a child to learn a particular rule. In the "phenomenological universal" approach, the potential is always latently there in the form of a universally pre-set "rule", but the child may learn to suppress that rule in case there is no epenthesis.
Dealing with obstruent codas, since we find a tendency that languages may only allows sonorants as codas (and we don't find that languages only allow obstruents as codas, disallowing sonorant codas), epenthesis becomes relevant in that one way to get rid of an obstruent coda is to insert a vowel (alternatively, delete the obstruent, or turn the obstruent into a sonorant). The usual rule-based account doesn't itself provide any theory-internal reasoning to the effect that one should insert a vowel after an obstruent coda, but the Stampean approach, which lists actual phenomena, has a way to say this. This is very similar to the approach used in Optimality Theory, that you say that what is universal is "a dispreference for obstruent codas".
I confess to not understanding the fine details of Stampe's approach, so it's not clear to me how he would express the difference between grammars of languages with vowel-epenthesis, coda-sonorization, obstruent deletion vs. no change. In Optimality Theory, the processes themselves are epiphenomenal as they are in generative phonology, what is universally available is something abstract (dispreference for obstruent codas; dispreference for changing segments; dispreference for inserting segments), and the actual outcome derives by the specific arrangement of these abstract potentials (you insert a vowel if you have changing consonants even more).
The heir of standard generative phonology, substance-free formal phonology, says that the question of why languages tend to have epenthesis rules that take obstruents out of syllable codas is not a matter that should be encoded in linguistic theory, rather, it follows from general facts about phonetics, historical change and language learning. This is the Hale & Reiss (etc.) approach. In that sense, the potential is "always there", but it is not hard-coded into the language faculty as part of grammatical theory, it's a more general cognitive thing.
I do know that Tarone holds (held) that CV is a basic articulatory and perceptual unit: dunno how that relates to your issue.