No! Its all in your control. If you want to let the Appreciate app access your SMS history, you can benefit from actual rounding of your transactions. However, if you don't want to do that, you can just set a daily SIP. The app won't get access to your SMS.
Psst. - even when you give access, SMS data never leaves your phone and are used purely to identify transaction details, solely for Change Savings purposes. So you can rest assured that your information is safe!