Yes. Momento is completely private. Everything stored in Momento is only visible by you. Nothing is ever shared unless you explicitly choose to share a moment using the 'Share' functionality within Momento.
Will adding people to a moment notify them?
No. Adding people to moments is purely for reference, allowing Momento to organise the moments in your life by the people you spend time with.
People you tag won't be notified of anything and moments won't be shared or accessible by them.