Is Salesforce NPSP Contact Sync Automatic?

Yes, it's automatic. Once the Salesforce integration is set up, Klaviyo checks Salesforce every hour and brings over new and changed Contacts on its own (help article). If a Contact's email already matches someone in Klaviyo, that profile gets updated. If not, a new profile is created. You don't need to click Re-import for everyday changes. As far as I know, that button is more for pulling everything in again after a big change, like new field mappings, but Klaviyo doesn't spell that out in the docs.

The one thing I'd check with NPSP is the email field. Klaviyo needs an email address to create a profile, so any Contact with a blank email in the field you mapped gets skipped. NPSP has a few email fields, like Personal, Work, and Preferred, so make sure the one you mapped is actually filled in on your Contacts. An easy way to confirm everything is working: add a test Contact in Salesforce, wait a little over an hour, then search for that email in Klaviyo.

I hope this helps and thank you for sharing your question here in the community.
Cheers
Arpit.