React-native: How to control what keyboard pushes up

The structure of the app is fairly simple: A searchbar, a listview and react-native-tabs at the bottom. The problem: If I click on the searchbar on Android it pushes the whole app up, so I see the tabs directly over the keyboard. But on iOS the keyboard overlays the whole app, without pushing anything up. Is there any way to control that?
I'm happy to share code / screenshots if the question isn't clear.
Thanks

edit:

<View style={{flex:1, backgroundColor:'#f2f2f2'}}>
    <ListView
        dataSource={this.state.dataSource}
        renderRow={this.renderSearchResults.bind(this)}
        style={styles.listView}/>
    <KeyboardAvoidingView
        style={styles.addQuestionBar}
        behavior={'position'}>
        <Text>
            Don't see your question?
        </Text>
        <TouchableOpacity>
            <Text>
                Add it
            </Text>
        </TouchableOpacity>
    </KeyboardAvoidingView>
</View>

Set android:windowSoftInputMode="adjustPan" in your manifest file, and it will work as you expect.

E.g.

<application
  android:name=".MainApplication"
  android:allowBackup="true"
  ...
  <activity
    android:name=".MainActivity"
    android:label="@string/app_name"
    ...
    android:windowSoftInputMode="adjustPan">
    ...
  </activity>
  ...
</application>

For those using Expo

@J KW's answer is correct but if you're using Expo you will have to implement it differently.

Expo uses different configuration terms. In your app.json you have to set the configuration key "softwareKeyboardLayoutMode":"pan" in your android object. Your file might look something like:

{
  "expo": {
    "name": "App",
    ...
    "android":{"softwareKeyboardLayoutMode": "pan"},
    ...
  }
}

Note: If you are receiving a "should NOT have additional property" error, it's likely because you don't have the updated Expo SDK (v.038). Please update your Expo version.

Documentation: https://docs.expo.io/workflow/configuration/