The way to parse the condition is
Highest scoring answer that outscored (an accepted answer with score of more than 10) by more than 2x.
This means that the conditions for an answer of score a to be awarded the populist badge is for there to be an accepted answer of score A, where
- a > 2 A,
- A > 10, and
- there are no other answers with score > a.
In turn, this requires that a≥23=2(10+1)+1.
If you are trying to dissect the history of a given post or badge, a useful tool is to use the post timeline*, which is of the form
https://physics.stackexchange.com/posts/1234/timeline. For the particular post you mentioned, the conditions were fulfilled at the end of June 3, with Ooker's answer accepted at score A=+11 and JamalS's answer at score a=+25. It is often the case that badge-awarding scripts run daily in the wee hours of the UTC morning, which seems to be the case here.
Another nice tool for exploring this sort of things is the Stack Exchange Data Explorer, where you can pose all sorts of SQL questions to the site database. To explore the populist badge, for example, you could use this query, freshly baked by yours truly, which turns up the posts which currently fulfil the badge criteria. It comes up, at the moment, with 16 rows, with two extraneous results (1, 2) that can be easily detected as outscored duplicates on the list. This is six posts short of the 20 badges currently awarded, and these no longer satisfy the conditions (1, 2, 3, 4, 5, 6), for various reasons that can be investigated via the post timelines. Just as an example of ways to test how the site works (and get some SQL practice along the way).
* Not particularly accessible or well documented. See here for an explanation and/or to complain about it.