Formally speaking, in 5e, effects are quite specific about their timing; there isn't really a 'round 1, round 2' situation, just an initiative order that progresses by individual character. The most common timings you see are "Until the start of its next turn", "Until the end of its next turn", "Until the start of your next turn" and "Until the end of your next turn". these are all quite specific timings that cannot be conflated with one another, because they affect the ability of many features to even be able to work at all.
When you knock a creature prone, for example, they cannot stand up until the start of their next turn - yes, this means that if it's *Just you and the target involved in the fight, and you only get one attack per turn, then there is unlikely to be any benefit in doing this (though there still may be: the creature will had disadvantage attacking you if you move away and provoke opportunity, and you may be able to move out of its reach, forcing it to spend its next turn dashing to get to you, for example), but in most cases, it's not just you and the target - there's your party to consider as well, and the creature should remain prone for all the turns between yours, and its, when it can stand up. If your turn is directly before the creature's, you can still work it to your advantage, in formal 5e, such as by using the ready action, to hold off until after the creature has just taken its turn - such as readying to knock the target down when your ally approaches to attack it).
Other effects, such as ones that cause stun, the timing will denote specifically that the stun lasts "until the end of the creature's next turn", specifically denoting that it will spend an entire one of its turns stunned, regardless of where in the initiative it is in relation to you.
Unfortunately, even since the earliest days of BG3's EA, we have been telling Larian that their handling of effect timing is very bad, and that the way they have implemented it globally causes major problems for the game. Every crowd control effect is saved against functionally with advantage, for example - a creature must fail twice in a row before you gain any benefit ,due to them getting the effect's save-out at the start of their turn, rather than the end, frequently causing a spell that did stick to still not have any actual effect or benefit. In the case of some other abilities, it's make them completely non-functional in their entirety, such as effects that only last one turn, but which time-out at the start of the target's turn, and so effectively last no turns at all, and do nothing, even when they 'work'.
Larian have been told again, and again and again, endlessly since the early days of EA that this is a problem, both in large threads and in direct bug reports, but they have never done anything about it in any way.
