TZ data doesn't factor into it. We should all be running TAI and UTC and all other timezones would just be TZ data from TAI, but what we are doing is we are running unix time, which doesn't support 61 seconds in a minute, with UTC as a reference, which requires it.

So what we do when there's a leap second, unless we have measures in place like Google and Amazon do (but in their own different fashions), is we're just suddenly running one second ahead of correct time and NTP will slow down our clocks a bit until we have compensated for that second.