I placed an order yesterday and got the invoice almost immediately by email. If you didn’t get one, that’s not normal. But it’s probably just a server that’d down or the email queue that isn’t flushed, if the Paypal payment went through. And you have an order number 
Actually, since I’m on the subject, I really wish the DT webshop had accounts, where one could enter one’s details once and for all, view previous orders and/or download invoices again.