I have a question about the app called Textfree with Voice!?

My boyfriend is in the states right now but I'm in South Korea. We both have iPhones and I got this app called Textfree with Voice (he didn't get it). My phone is on airplane mode because it keeps turnin on roaming by itself and I don't want to pay for roaming. I text him using ONLY wi-fi and when i text him he gets it like a regular text mesaage because he didn't download the app. And when he texts me I get his text through the app. Im sure you know about this app if you used it before. Anyway, will this charge him any extra fee to send me texts since he's texting abroad even though Im just using wifi???