That looks suspiciously like something you'd find on wikipedia which is only citing voting age population instead of voting eligible population as it claims. i.g. in 2016, there were 250 million people over 18, yes, but only 230 million of them were eligible to vote. So, 55% of adults voted, but actually over 60% of eligible voters voted in 2016. And in 2008, what you posted above of 229 million eligible votes is also just the voting age population, but the voting eligible population was closer to 213 million. The sources i used is the US Elections project and another presidency project by UCSB which has nearly the exact same numbers.
Just looking at the last 50 years the two highest are 2008 at 61.65% and 2016 at 60.1%.
So that was forefront on my mind. Lately it has not helped the incumbent party. 3 of the top 5 highest voter turnouts by eligibility went against the incumbent party. Those being 08, 16, and 92. But it's happened 6 times out of 10 elections. So me saying 'not usually' is more accurate than the sentiment you are projecting in your post though.
For posterity the top 10 highest voter turnout elections, as a percentage of eligible voters
- 2008: Barack Obama v John McCain (61.65%)
- 2016: Donald Trump v Hillary Clinton (60.1%)
- 2004: George W. Bush v John Kerry (60.1%)
- 2012: Barack Obama v Mitt Romney (58.6%)
- 1992: Bill Clinton v George W. H. Bush (58.1%)
- 1972: Richard Nixon v George McGovern (56.2%)
- 1984: Ronald Reagan v Walter Mondale (55.2%)
- 1976: Jimmy Carter v Gerald Ford (54.8%)
- 1980: Ronald Reagan v Jimmy Carter (54.2%)
- 2000: George W. Bush v Al Gore (54.2%)