I've seen a few other people have this problem, but I don't have any errors showing up.
When I go through to test the checkout process of my pianoteacherpro.com website, everything seems to work right at this point, there's just no creation of a new wordpress site.
You can check it out yourself. I have a free product up for testing right here.
I went through all the steps for installation, (it took me a few times to get it right) and I have the servers set up, products set up, modules added and all.
After I check out, I get a welcome email from WHMCS but nothing from Wordpress and no new sites are created when I check the super-admin area under "sites".