WWYR - Difference between announced cost and resolved cost
So he announced “For 7” which is often seen as X=7.
He tapped for X=5.
He resolved for X=4.
You'll need to intervene alright, as regardless something has gone wrong. The next step is to figure out what went wrong.
(a) If you believe he clearly announced X=7, then you have a case of not paying the costs correctly (just like the IPG example of paying 3W for Wrath of God instead of 2WW). The fix for that would be to rewind, which includes shuffling the cards seen off the trigger back into the library.
(b) If you believe the reference to 7 meant GG plus X=5, then he has failed to properly resolve his trigger. Since he's still resolving the ability, just have him reveal the 5th card too, choose, and assuming the hydra resolves, add the 5th counter.
© If you believe he has just overtapped for a perfectly legal X = 4 and hasn't announced floating mana, well, that's probably not the case. It sounds much more like he paid 7 mana for a 6 mana spell, which again is paying the incorrect mana as above. Rewind, including shuffling seen cards. Yes, sure, players can float mana. But I don't believe that's what he's done here, so he's not guilty of not announcing floating mana.
If he just tapped 7 lands, then we're at solution (b).
If a spectator calls you it's much the same as above, with a thank you to the spectator.
In all cases, I'll say to Nestor that it's better for him to speak up when he sees an issue, even when a judge is there. This is because the judge hasn't been playing the game, so may not be up to speed on everything that has happened; the judge may not be familiar with the cards to know immediately that something is wrong; or the judge may have been nearby but actually watching something else so may have missed it. Ultimately, I don't want the player to see an error, have the judge miss it, and for the player to leave with a sour taste in his mouth because the judge failed him in some way. Speak up! We won't bite!
Lastly, I'm happy for players to put counters on their hydra before properly resolving the trigger, even though it's the wrong order. So long as they make it clear that they're resolving the trigger and haven't forgotten it I'm not going to stop the proposed shortcut or argue they've missed the trigger, just because they wanted to keep everything clear.