Summer Savory (herb) is classed tender in the cited extension guidance. The timing rules below are relative to your local freeze dates — enter a location to turn them into calendar dates.
The rules this site applies
Method
Frost-relative window
Rule & reconciliation
Start seeds indoors
6–4 weeks before the median last spring freeze
Illinois Extension allows about 4 to 6 weeks to produce summer savory transplants, and those go out after danger of frost is past, so sowing runs 6 to 4 weeks before the last spring freeze.
Transplant outdoors
from the median last spring freeze to 2 weeks after
Illinois Extension transplants summer savory after danger of frost is past, matching the Texas A&M sowing cutoff, so the window opens at the last spring freeze.
Direct-sow outdoors
from the median last spring freeze to 2 weeks after
Texas A&M AgriLife Extension's herb publication directs seeding summer savory after danger of frost, a point rule that opens a two-week sowing span at the last spring freeze.
Variety assumption: Illinois Extension notes summer savory can be harvested within two months of sowing, so one spring sowing carries the season.