Daylight Savings Time Screwed Sync and Nothing Fixes it

The fact that AnkiDroid differs from the desktop when the legacy setting is enabled is an AnkiDroid bug that they haven’t gotten to the bottom of. Switching to the new timezone handling may cause Anki to shift forward or back a day (which I presume is what you mean by “correct”), but the new handling is intended to better handle future changes in timezones, so I’d recommend you bite the bullet and switch to it.