This post is primarily a bump.
However, I now have access to Tactical Operations: Advanced Rules (2020 printing). The rules for smoke are now on pages 45-46. The sentence in question, now on page 45, remains unchanged.
For possible clarification, I think my confusion is related to the use of the phrase "only start to determine", implying a delay before checking for dissipation the first time. However, as written, it seems that the first dissipation check is made during the End Phase of the turn in which the smoke was placed on the map, since said End Phase is "following" the turn in which the weapon-delivered smoke was placed on the map. Is this as intended, or should it be the End Phase of the turn following the smoke being placed on the map, i.e. the End Phase of the turn after the turn in which the smoke was placed?