If you don't play the account the hirelings, they don't send mails, if you have them in your main account, like I do, they deliver promptly.
I've had to login to each individual character that has a hireling for it to deliver. It doesn't seem automatic if you just play one character. I have 5 characters with hirelings for Blacksmithing/Clothing/Woodworking on each, so I should get 3 deliveries per character, thus a total of 15. I get none on my main, I have to physically log onto each character to get the 3 and then I log onto my main and finally see the 15 delivery mails. It is the only way deliveries have been working for me.
Maybe that is how it is supposed to work, but since all characters share mail, seems a bit sketchy to me (waste 10 minutes logging in and out just to receive shared mail).