Hi James,
Thanks for using WooCommerce Tickets. I can troubleshoot this with you.
WooCommerce does not send the Tickets or the Order Complete email until an order is manually marked complete.
There is a plugin called WooCommerce Autocomplete Orders
https://wordpress.org/plugins/woocommerce-autocomplete-order/
This marks all orders complete on successful purchase and will then send out the tickets and Order Complete email.
Let me know if that works for you or you are having issues beyond this.
Thanks