Judging by the recent Haula trade, the NHL Central Registry will look through the trade proposal and if the wording of the condition leaves room for vagueness, they will clarify it.
In the Haula trade (VGK -> CAR) there is a conditional 5th to be moved in various scenarios, and CR took their time looking into it because there was some unclarity what happens in a specific case.
As the Duchene trade was accepted by CR, there assumably isn't anything unclear in the wording. It is another question if we the hungry public actually get the exact and correct wording of a condition, BUT:
if the condition says "re-signs" (and nothing else), the CR probably had what happens in this scenario clarified up between the parties;
if the condition says "extends", then July 30th would clearly be the deadline.
So, what's the exact wording?
edit: NHL.com reports: "the Senators would receive a conditional first-round pick in the 2020 draft if Duchene signs a new contract with Columbus."
Seeing that expectation probably was that Duchene will see what's there in the Free Agency, this wording would suggest that any new contract signed between Duchene and Columbus will trigger the condition on the pick.
editedit:
but CapFriendly knows to state about the matter:
"**Conditions: If Duchene re-signs with the Blue Jackets, Ottawa will receive Columbus' 2020 1st round pick. (If the 2019 pick moves to 2020 as a result of the lottery and Duchene signs with Columbus, the 2020 conditional pick would then move to 2021). If Duchene does not re-sign with Columbus, no pick is exchanged."
"
Result: Duchene did not re-sign with Columbus, no pick is exchanged"
Matt Duchene Trades - CapFriendly - NHL Salary Caps
So it's a very good question, and the answer is that the goddamn journos including the ones at NHL.com oughta do their jorbs.