If you order bulk topsoil and the company delivers something else like mulch, do they take the misdelivered stuff back or what?

Put a tarpaulin over it until Tuesday. 

Its too late. The labor to scoop it up and haul it off cost more than the delivery. You should've refused delivery upon arrival and inspection of the stuff before it was dumped. But it also depends on the companies return policy and how much they want to keep you as a customer.

Try being more specific when ordering, or inspect the source before ordering.

Did you look at the pile of topsoil that they were to deliver or are you arguing what you think and what they think is topsoil?  Mulch is often referred to as topsoil because you mix it with your existing dirt and get topsoil.

Mulch will just be wet mulch if it rains. It's not going to spread. They have to clean the mess up and take it away. 

It's their responsibility to deal with it.  If it rains, then you have a bigger issue on your hands.  You could try to claim it washed into your yard and they owe you damages, but good luck on that one.

They had better.