Indigo - Flight left without announcing boarding closure and charged for arranging another

We had a connecting flight from Agartala to Chennai via Kolkata. The first flight was scheduled to arrive at Kolkata at *.** am but it was late and reached almost at ** am. Then my father and mother who are patients went quickly and were done with security checkin too. Then went to washroom due to emergency and reached at boarding gate at **:**. The departure time was **:**. The staff called and said flight already departed. What kind of service is this where passengers already were done with security check in and the flight was a connecting flight with same PNR and then also without announcing and calling prior they left ** min early. Indigo now a days are so irresponsible that they only think of how to charge customers more and more. When a passenger are done with security checkin it means they are near, the staff should call and should take responsibility to board them specially the senior citizen. But they are not at all responsible and then charged my parents. It was their fault that the first flight was late by almost half an hour and the time duration in between changing flights was very short, which is chaotic for old passengers to run, and go through the busy security check-in. But after all these also the Indigo staff were so irresponsible that they did not call prior and neither announced the gate closure. I want a refund or anything similar to my loss. And such behavior of Indigo should be stopped. We, the passengers, are booking connecting flights because its safe that if flights are late, they will take care of it, but Indigo nowadays are too much into charging people and not taking any kind of responsibility.