The waiting time will be ~40 seconds if it's an early text or ~50 seconds if it's late. There's no way to know what it's going to be.

You had to wait forever in the first video because the activity call came in the moment you entered the cab. This pushed it back another ~35 seconds. You then pulled up the phone which delayed the next message even more. LJ's call delayed it again. The second video shows a late text.

You should always cab to your next destination and aim to guarantee texts.