In NetSuite, navigate to Setup > Accounting > Accounting Preferences. Under the General Ledger section make sure that the field Allow Transaction Date Outside of the Posting Period is set to Warn.
You can then select if you want your reports to export to the First Open Period or the Current Period.
Also, you'll want to ensure that the Export to Next Open Period feature is enabled within the integration config in Expensify. Navigate to Settings > Policies > Group > [Policy Name] > Connections > Configure and open up the Advanced tab. From here, confirm the setting is enabled:
Without this setting enabled, you won't be able to export a report to the next open period if your settings in NetSuite are correct.