Hyper Intuition has a lot of weird showings and feats that most fans just forget about.
Like when Tsuna saw Mukuro's memories in varia arc.
Or when he read Enma's mind.
Or Tsuna and Enma coming up with a silent plan in the middle of a fight without them ever talking about it or fighting side by side in the past.
Or when he understood Daemon's lover's emotions and knew what she wanted to say. Despite her being long gone, and maybe not even a ghost anymore/not on their current realm. Since Daemon couldn't communicate with her, even in his soul form.
Then there's even weirder feats. With Tsuna just knowing stuff without any actual explanation (Not even a supernatural one). Like what actions someone from far away would take, him knowing who it was that sent him and everyone else to the future, and knowing that Chrome was the person who had a powerful ring at kokuyo land. All things he really had no way of knowing even considering his previous feats with Hyper Intuition.
How stuff like this would even interact with someone seeing a few seconds into the future is difficult to judge. Innately knowing of things without even sensing them, like Tsuna has displayed in some instances, is practically the same as actually seeing the future.
You could argue that most of these might not transfer over to battles, but who knows? Just because it isn't brought up in every fight, doesn't mean it isn't there (And some of these are indeed fight situations. Scratch that, most of these are in base mode, where it's stated that his Hyper Intuition is much less potent than in DWFM). The same thing happens in OP with sensory haki, from what I've heard. With people being stated to use it, or only really shown to explicitly have an aspect of it once or twice.