I submitted the BVI Gateway applications for 2 vaccinated travelers at 4:47 and 4:57pm on Monday. Received both approvals Tuesday @ 12:37pm, less than 20 hours later and 4 days prior to departure.

Seems like the automated approval is probably in place and working.

I should also note, I used the proctored BinaxNow tests from eMed.com taken on Monday afternoon for a Saturday arrival.