If Jago has you in a grounded combo state, and you break his combo, the combo break forces Jago into a flipout, which is not a soft or hard knockdown, and as such, the moment he touches the ground, he is able to continue his pressure. The reason why it’s more dominant with Jago is that a good bit of his game relies on that pressure and his shadow windkick is strong pressure being positive on block, as well as traveling forward very quickly within a small timeframe. It’s a great way to close the gap quickly created by the combo breaker to regain momentum.
However, this isn’t limited to just Jago, but any character that’s combo broken in a grounded combo flips out, which leads to a reset to neutral for both players (usually) at the same time, can pull off shadow moves the moment they touch ground, and so you have to be prepared to react appropriately. I can do the same thing with Cinder’s Shadow Trailblazer (and have several times) on being combo broken to continue my pressure strings.
That said, if he’s juggling you while you are in the air, and you break his combo, he goes into a soft knockdown, which puts you at a slight advantage.
In the event you combo break Jago, and you know he has meter, then you need to be ready to react appropriately. I see a lot of people make the mistake that this is Street Fighter and try to mash jab on wakeup as a counter, but it just doesn’t work on shadow windkick. The best idea would be a preemptive neutral jump to jump over it and counter upon landing, or if you are spaced correctly for it, a jumping neutral cross up could work too, depending on the situation. If you have meter yourself, you should probably try to block it, as the chip damage isn’t that high, and then shadow counter. Shadow windkick is one of the easier moves in the game to shadow counter, and makes predictable Jago’s pay with strong punishment. You could also try a DP style move, but that has the potential to trade rather than win out, depending on your character.
So in short, Jago’s not the only one who can fight back the moment he touches the ground. Any player who’s been flipped out, like in a grounded combo breaker, can begin their assault the moment they touch the ground, but there is no combo breaker in the game that leaves you vulnerable and lets them hit you free if you combo break correctly. No matter the character, you will be able to at least block, so if you are getting hit after breaking, you may be trying to counterattack with something ineffective and you should look for an alternate counter for the situation.
It’s tough to deal with sometimes, but Jago’s a pressure character. Now that his damage has been toned down somewhat, his meter build and damage ratio is much more fair. Hit up training mode sometime, record the situation, and try some different counters to see if you can find something more reliable to counter.