No. As long as you use the same Google Account, paying on one device is enough.
On the other device, open the menu (≡) → "Premium Service" and tap "Restore" (for users who purchased before). The Premium Service becomes available without paying again.
If restoring doesn't work, check your network connection and make sure the account signed in to Google Play is the one you purchased with, then restart the device and try again.
If it still doesn't work, you can choose a plan and go through the purchase again. With the same Google Account you won't be charged twice, and the Premium Service will be activated.
* Your notes are not synced automatically. To share data between devices, create a backup with "Google Drive Backup" and restore it on the other device.