Let's check those against dictionary.com (tiny disclaimer: this seems to be slightly biased towards US, not UK, English)
sin~~cere~~~ly > sin·cere·ly
ox~~~y~~gen > ox·y·gen
sep~~~a~~rate > sep·a·rate
in~~vin~~ci~~ble > in·vin·ci·ble
un~~e~~~ven > un·e·ven
… and this is from the online Help, on the use of tildes to indicate good/worse hyphenation points:
“If you don’t like the hyphenation points, follow these guidelines to indicate your preferred hyphenation of the word:
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Type one tilde (~) to indicate the best possible hyphenation points, or the only acceptable hyphenation point, in the word.
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Type two tildes (~~) to indicate your second choice.
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Type three tildes (~~~) to indicate a poor but acceptable hyphenation point.
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If you want the word never to be hyphenated, type a tilde before its first letter.”
So it would seem ID doesn't do too bad, and it's just a matter of personal preferences. Now those cannot be selected in ID's Preferences panel.
By the way, if your proofreader objects against 2 first or 2 last characters before/after a breaking point, you should change that in your Hyphenation settings. Those are there for exactly this reason.