I can't receive SMS text messages from non-iPhone users until I turn on cellular data?

I can't receive SMS text messages from non-iPhone users until I turn on cellular data?

Added (1). I have an iPhone 4S on Page Plus. If I turn off cellular data, I don't get any SMS text messages from non-iPhone users. Even if my Wi-Fi is turned on, nothing comes in. When I turn cellular data back on, the text messages flood in. I'm updated to the latest IOS version.

Added (2). I'm positive I'm just turning off data. They are individual conversations.

Are you sure you're just turning off your data connection, and not your entire cellular connection (a la airplane mode)? Also important: are these text conversations with just one other person, or group texts?

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