There are three ways to add contacts on Tinkle for Web.
Shared are your business contacts, which all of your company will have access to. These can only be added by admin users via Tinkle Business Manager.
Address Book is for any personal synced contacts saved on your company. You can add a contact by clicking into Manager and heading to the Contacts.
365 allows you to sync your office 365 contacts to the Tinkle app. To do this, head to Settings and then Accounts. Log into Office 365 and provide the relevant credentials.