If you haven't done this already, check your settings and make sure that in Messages "Send as SMS" is on. If that doesn't work...
Are you seeing a failure to send message on your phone? If you press that "i" in the red circle, you might see an option to send as plain text. Also, when you are texting to other iPhone users, if you press the message you've just sent, you should see a bubble come up above it with the option to send as plain text. If you press that right away, the message will go as text. Texts in blue bubbles and with the "Send" in blue are going over the internet (iMessage server), which you won't have with your data shut off unless you're on wifi. Texts in green bubbles with the word "Send" in green is going as a plain text message.
I know the iMessage thing can get convoluted and confusing and annoying...DH and I went through the same thing with our iPhone 5's.
We have iPhones from Canada and we're in the U.S. for the winter. We turn off our cellular data when we're here, but we have wifi in our condo. His phone was OK, he was getting texts from his Apple and non-Apple contacts whether we were at our condo or not. I, on the other hand, found that texts from my Apple contacts weren't reaching me until I was on wifi, so they were coming over iMessage (which is internet) instead of as texts.
I determined that the issue was because I have two other Apple devices which receive iMessages from my Apple contacts as well, and when these devices were in our condo on wifi, the messages from my Apple contacts reached my devices. The iMessage server considered them as delivered. Had my other devices not been on wifi, iMessage would have kept trying to reach me and after not succeeding, would have delivered the messages as texts to my iPhone. If I want to be reached in a timely manner when we're out, I would have to turn off wifi on my iPads before we left the house.
Sometimes DH would be out with his iPhone and texting me. His texts came as texts, not iMessages, because he was not on the internet with his data plan turned off. At home, my iPhone was on the internet over wifi. When I replied to him, my phone tried to reach him via the internet (iMessage) because he was an Apple contact. iMessage will try to deliver the message and when it doesn't reach the destination device, it will evenutally send it on as plain text, but it might take some time.
There's more info here:
http://apple.stackexchange.com/questions/140954/why-do-text-messages-not-appear-when-off-of-wi-fiAnd:
https://discussions.apple.com/thread/6539721DH and I never paid any attention to the differences between texts and iMessage when we were in Canada, although we did wonder why some messages were in blue and others were in green. We have generous data plans on our phones (a soft cap of 10Gb each phone, and speed would be slowed if we went over rather than being charged extra $), and the phones seemed to switch seamlessly between iMessage and texts going by our cell phone carriers. I don't know if iMessage used much in the way of cellular data unless we were sending pictures (which we like to do, but here in the U.S. we can only send pictures by message to our Apple contacts and only when we're on wifi).
I hope you find something at the above links helpful.
