On deployment, I want a separate sheet created for each user.

[Dubams]

How do I ensure that each user can only access their own data when I share my app with them on appsheet?

I have built an expense/income tracking app that records a user's cashflow within a month and displays on a summary view. However, if I share the app with someone else, they all edit the same set of tables. 

How do I make sure each user has his unique data set when app is shared or deployed?

[TedM]

Basically they will need to log in (so it can't be a public app) and you need to add a security filter based on their login email address.

That will show them only their data.

Security filters: The Essentials

[Steve]

Limit users to their own data - AppSheet Help

[Dubams]

I was hoping there'll be a simple way of recreating the whole data set just like when I'm working with one of appsheets templates. 

I guess if I make it a public app or share as a template, users can "look under the hood" and modify the app with their own data. As opposed to my using slices and security filters to limit what users can access while having access (as creator) to the whole data set on my google sheet.

I want the app to run like the user has downloaded it from an appstore and has 100% control over both app data and google sheet data.

[WillowMobileSys]

This is a concept known as "Private Tables".  You can get more details here.