i think this is carrier issue, you'd have to talk to your carrier first.
If you and the other person is sending txt's practically at the same time, it really depends on who has better connection from what I understand. But if you or the other person sent message like 10+ minutes ago, and is doing what you described... it's certain an issue that might be worth mentioning to Samsung Members app post recreation of the issue (as best you can).
But... either way my suggestion is talking to the carrier first. With that said who's your carrier?