the word 'shortly' can refer to differnet time periods, it's contextual. In January I might say that it will shortly be spring, and everyone would understand. At two in the afternoon I might say it will shortly be teatime, and everyone will still understand.
In your case I agree with you that being told on a Tuesday that I would shortly receive an email about delivery of my order would tend to make me expect it by Thursday at the latest - maybe Friday if I stretched it.
If nothing comes by Monday I think you'll have to find time to phone PCW.