An outcome came within a hair of happening; the gap left was one small point and it did not (or only barely) tip over.
框 · Frame
差一點（就） [outcome] · optional 就 binds the outcome tight to the brink it nearly crossed
觸 · Trigger
An outcome was right on the brink — one tiny margin from landing — and you report that it nearly came (and usually that it did not).
序 · The move
1Name the outcome that was on the brink — the verb phrase that almost landed.Was it truly a near miss with a margin left, not something that fully happened? A done thing takes plain 了, not 差一點.
2Put 差一點 in front of that outcome to report the gap was one small point.差一點 measures the shortfall as a single hair; 差很多/差得遠 would say the gap was wide.
3Drop 就 in after 差一點 to press the outcome right up against the brink it nearly crossed.就 tightens the link; without it the line still reads, less pressed.
例 · Examples
1他差一點by one small margin — a near miss就presses the outcome against the brink遲到be late了the brink reached, the change registered。
Same 差 measuring the same gap. 差不多 reports two things come out about even (a steady comparison); 差一點 reports a single outcome that nearly tipped over and usually did not. About-the-same vs came-within-a-hair.
快要…了
快要…了 looks forward — the event is on its way and about to arrive. 差一點 looks back — the event was on the brink and the moment has passed. Imminent future vs narrowly-missed past.
幾乎 is a flat adverb 'nearly' with no relief; 差一點 carries the close-shave verdict that the margin was decisive. For an undesirable outcome, 差一點(就)遲到了 reads 'almost late — but on time', the relief built in.
✗ 他差一點到了，所以他到了 → ✓ 他差一點就到了 (沒到) (差一點 names a near miss; the outcome did not actually land)
✗ 我差一點考一百分 → ✓ 我差一點就考一百分了 (the outcome needs its tail — 就 + 了 close the near miss)
✗ 他差很多就遲到了 → ✓ 他差一點就遲到了 (the margin must be one small point; a wide gap is no near miss)
English 'almost' floats freely and stays neutral ('he almost arrived'). The learner forgets 差一點 names a measured one-point margin and, for an unwanted outcome, that 差一點遲到 and 差一點沒遲到 BOTH mean 'almost late, but on time' — the desired result survives either way.