Edit: OK, just re-read some docs, looks like POSIX chose the worst of all options and decrements the timestamp experiencing the same second twice...
Wrong info from before edit: Unix time doesn't change either, it's the number of seconds since 00:00:00 UTC on 1 January 1970, though systems may or may not ignore that and set it to match the UTC time.
Yes. It does. Op is correct. A leap second specifically is an adjustment because “how many seconds since 1970” changes because the earth’s rotation isn’t constant speed. UTC tone definitely changes. If it didn’t then you wouldn’t hear anything about it and it would just be transparently folded into your time zone database.