If you stay with the same operating system, and the same Google, or Apple account: no.
There are two versions of the app on Android: the free version is called Salsa Anywhere, the payed version is called Salsa Anywhere - Pro. Make sure you download the correct version on your new device. (You can check in Google Play, under My Apps which version you had before.)
After installing it, tap 'Buy more videos' and you should see that your old purchases were restored.
Just download the app from the App Store. Tap Unlock, and tap Restore. Your previous purchases will be restored, and you will not be charged!