The article is needlessly unclear, but the specification given in the second blockquote is the one that is actually applied, and a simpler way of explaining it

The article is needlessly unclear, but the specification given in the second blockquote is the one that is actually applied, and a simpler way of explaining it is: POSIX time() returns 86400 * [the number of UTC midnights since 1970-01-01T00:00:00] + [the number of seconds since the last UTC midnight].