Updating New and/or Existing Constituents is set on a field by field basis, so you'll need to review which fields you do (and don't) want to update.
For fields that you only want to update on New Constituents, you'll want to open the Field Settings (the red/green radio button at the end of the row where you've mapped the data - showing First Name as an example):
When you open it, it looks like this (you can see that the option to update Existing Constituents has been unchecked):
You can also work with entire mapping areas via Area Settings for mappings such as Addresses and Phone Numbers/Email addresses. These allow you to select data that constitutes a Match between the records in RE and the records in your data source. That way, you can determine if you want to update the information in RE, add the information as a new record or ignore it when the data matches.