Invoices paid using Indy's online payment processors, Stripe and PayPal, will automatically update. However, if you received payment for your invoice using an offline option, you will need to mark the invoice as paid when payment has been received.
To do so, click the 3-dot menu next to the invoice and select the 'Mark as paid' option. If your invoice has a deposit, you will also be able to mark the deposit as paid.