When you go to Download Sales Report on the dashboard, it brings up the Net Revenue Sales Report. You can select 'Date of Invoice' as you say, and the date range defaults to the last complete calendar month (currently 1st March to 31st March 2019). Any sales invoiced between those dates will show in the list of sales. Most users tweak the 'To date' to the current day as that shows you the most recent sales. In fact, if you refresh that report at intervals during the day it shows sales pretty much in real time, a real boon for sales hit junkies like myself.
When Alamy invoices the customer it shows up in this report. However, as Alamy works as a traditional photo stock agency, they offer credit terms to many customers which means the payment isn't actually due until some six weeks after the invoice date. When the customer actually pays the invoice the date of the payment appear in the left hand column as'cleared'. Once that occurs the amount will show in your 'current cleared balance' on the main dashboard.
The best way to see what has been happening on your account is to use the Net Revenue Sales Report and set the date range from as far back as you like (eg.the beginning of the year) and the 'to date' to be the present day. When you click go it will show you all your invoiced sales in that period and the ones where the customer has actually coughed up the cash will have a 'cleared' date next to the sale.
Once your current cleared balance exceeds $50, Alamy will automatically pay you by your chosen payment method.