It is likely that the times that Stout and Arisumi determined will strongly depend on temperature as it affects plant growth.
Arisumi did a simple test of the time period. He wrote "In greenhouse tests (unpublished data) with 13 crosses among daylily cultivars, averaging about 20 flowers per cross, it was observed that no seed was obtained when the styles were cut off close to the ovaries at any time up to 1O hr after pollination. So it requires more than 10 hours - presumably the longer the time the more seeds are produced (up to some limit).
Arisumi also wrote (from other research), "In crosses among fertile diploids, syngamy was observed in 24- 48 hr". Syngamy is fertilization - the fusion of the two gametes.