Before we start, I should explain for non-Korean speakers how coda-position ㅅ ("S") is pronounced in Korean. First, as jogloran has already hinted at, Korean has a tendency to avoid codas, converting them into onsets wherever possible (i.e. if the next syllable has no onset). Slight simplification but good enough for now. Second, ㅅ ("s") when pronounced as a coda (i.e. the syllable is pronounced in isolation or the following syllable has a non-null onset) it loses its [+stri] feature and is pronounced more like a soft (unaspirated) "t".
The point being that 인터넷 ("internet". Literally "intheneys", pronounced "intheneyt") is pronounced in isolation in more-or-less the same manner as the English "internet". However, again as jogloran noted, when followed by a null-onset syllable, as in 인터넷이 (intheneys-i, internet-SUB) or 인터넷에 (intheneys-ey, internet-DAT, "to/at the internet") the coda ㅅ adjoins to the following syllable as an onset and does not lose it's [+stri] feature. This results in the surface forms "in-the-ney-si" and "in-the-ney-sey" respectively.
It is important to note that several codas undergo the same reduction as ㅅ. Namely, 밧, 받, 밭, and 밪 (pas, pat, path, and pac respectively) all have the same surface structure: 받 (pat). Of these "t" codas, ㅅ is by far the most common.
Therefore, Koreans most readily associate "t" codas with ㅅ. From here it is not difficult to imagine why ㅅ used as a "t" coda, even in English loanwords.
Loanword adaptation as first-language phonological perception. by Boersma and Hamann is a paper I have heavily cited on this website. Essentially they propose that a learning algorithm dynamically ranks OT perception constraints over time such that rules preventing specific phonetic units from being perceived as specific phonological units become ranked in such a way that valid perceptions (for example
*[a]/a/, "don't interpret the phonetic
[a] as the phonologic
/a/" becomes lowly ranked because it can be violated freely with no loss of meaning).
Essentially, this paper provides a mechanism by which Koreans can perceive phonetic [t]s in the coda position as the phonologic /s/ (since the constraint forbidding this perception becomes lowly ranked). The result is a UR containing the /s/ coda which then explains its production as [s] in cases like "인터넷이". This UR /s/ is then reflected in their orthography.