I will try to give you my recent experience with entering / departing the DR within the last month.
I arrived in the DR via JFK to STI airport on July 27th with an DR entrada eticket prepared and presented it to the immigration officer. At no time did he even looked at it, however after scanning my BDA passport, all photos and entrada info appeared on the screen, He asked me only to confirm how many days I would be staying, stamped my passport and said; bienvenido. I asked him if I should leave the eticket with him, he said no for me to take it.
Next step after collecting my bags was to stand in a long line with 60 -80 Dominicans waiting to pass thru the scanner to exit. As I waited I could see in the middle of the 2 scanners a group of people filling out the custom form before having their bags scanned. Then there was an custom agent asking everyone in the line if they had an eticket. I raised my paper copy and he took me to the front of the line, scanned my code, and then told me to leave after placing my bags thru the scanner, He gave me back my form, and BINGO out the door...
Fast forward to leaving today the 23rd of August on the redeye 1:55 am flight back to BDA via JFK. Arrived at STI airport early, checked in and the ticket agent looks at my antigen test results, and and takes my US signed form and places it in her draw, the one that everyone is required to present to the airlines to prove a negative covid 19 test has been done within 3 full days of departing. At no time did the agent ask for my salida eticket. She gave me back my lab result form and I was on my way via immigration with boarding cards and passport.
As I approached the immigration station with once again my salida eticket form in hand, I noticed 20-30 travelers to my left at the wall counter filling in the arrival/departure forms by hand. I gave the agent my eticket with passport and again she never even looked at my printed form. Swiped my passport, and again photos and departure details (especially the date) appeared on the screen. She stamped my passport and said; have a safe trip, especially as New York is really bad with storms
I know mainly STI receives a large % of New York and Miami Dominican travelers living in the US, however I have always felt that they are way more professional in their security and procedure approach than compared to say POP, by a long shot. Just ask anyone that works at POP airport about the lab results for the antigen test that are being done for the same day travelers entering the USA, and that will tell you all that you need to know about how that airport operates. But getting back to the eticket requirements, it seems to me there is a direct link to one's passport number with the information which is pre loaded before arrival/departing the DR. That and because the eticket has no entry or departure requirements to the airlines for the DR, why would anyone be denied a airlines boarding cards?