When you select it in basket there are links to the information. They will ship the S4 to the hosting directly, but you also need to make an account with Umisoo.
That part I have done. I'm talking about once you log in to Umisoo. Tracking number shows they received it yesterday.
When I log in, it doesn't show any hardware but if I go to the "My Order" page, it shows an unpaid order for ~0.33 BTC. It also says "You must make a payment within 1 hour, or your order will be cancelled."
So my question is, am I supposed to pay that invoice before they actually start the mining? I'm worried because it most certainly has been more than an hour since I didn't even know that was there.
Yes, you should pay monthly hosting service fee upfront. (This support for Umisoo is unofficial)