Are you suggesting that the characters are actually forced to stop moving between turns?
It's not like your character literally stops at the end of their turn and waits for everything else to happen before they resume movement. If you need to make a long jump, and you used your full movement in the previous round, then you were moving immediately prior to making the jump.
The rules of the game - the round structure, and the jumping rules - describe what's going on within the narrative. They don't define it. And in this case, it should be fairly clear as to what's happening within the narrative, and why the rules allow this type of movement. (Less clear is how these boots mysteriously know about the concept of rounds. It seems likely that this unnecessary line was just included in hopes of expediting gameplay.)
I'm not suggesting anything; I am asking a question about a particular rule, because assumptions are being made that seem neither to use natural language, nor to understand a word like "immediately" the way it is used elsewhere in the book. (e.g. "The spell effect ends immediately" does not mean at the end of your turn, or the end of your next turn.).
So -- to do a running long jump, you need to move 10 before jumping, and yo are both implying (if I understand you correctly) that the ten feet can occur in the previous turn.
If that is so, that's a new understanding of "immediately".
Let's say someone does move 10' in the previous turn, and then they attack. Can they still do a running long jump next turn, using that 10' of movement? I'd say obviously not. move--attack--end of turn--jump. The jump is not "immediate" by any sense.
Let's try again. Someone moves 10' in the previous turn, and then they are attacked. Can they still do a running long jump next turn, using that 10' of movement? Again, I'd say obviously not. move--end of turn--get attacked--possibly take damage--jump. The jump is not "immediate" by any sense.
I can see why you might want the move to occur in the previous turn, and why that might make sense *if* the character is not attacked, or makes any checks, etc. But the plain reading of the text, as far as I can see, is as I described above: on your turn you move ten feet, do not attack or take another action, and then begin the jump.
I'm not trying to force this interpretation onto anyone, and (as I also suggested) there are tweaks to the rules that help make this rule more natural in play. But the situation is not clear, and this ambiguity supports the OP's point about the weakness of the magic item.