Ideally the individual spirits should die with some time apart so as to prolong the duration of the buff as much as possible.
The Skeletal Militiamen Ashes trigger this talisman every time they are reduced to 0 health, even if they manage to resurrect themselves afterwards, which is a very strong combination.
An unupgraded or minimally upgraded spirit ash can theoretically make it easier to use this talisman, as they'll live for a much shorter period of time and therefore activate the buff much more quickly.