It sounds OK. Mother tongue is just a synonym of native.

I suspect it's a direct translation from Italian. And no it's not correct. We say"native speaker"... But, maybe we ought to update it? Why? Well, when I first heard the Italian phrase it seemed a very Italian way of thinking about the world and a bit outdated to me. There's plenty of people living in Italy now who's first language is Italian but who's mother was not born in Italy. And then when I thought about it a bit more I thought that there's also plenty of people who aren't native to the UK but moved there when they were little and certainly do speak English at the same level as (or better than) people who were born there and who's families have lived there for generations. Not sure what phrase we should use.

"Their mother tongue is english" would be better

The expression uses "mother tongue" (a noun) as an adjective. It is not wrong to do that. ANY noun can be used as an adjective, but you should be careful not to do that too much. For example, you could say "she is a girl English speaker" and it would not be wrong. It would only be OK, not great. It is best to use "mother tongue" as a noun that names a language (and not a person): "English is her mother tongue". Never use it to name a person. Never say "She is a mother tongue".