A "630W" PSU... the real number would be 588W, that being the max power output on the +12V rail. It's a crappy unit with no reviews from any reputable reviewer.
I'd just swap to a better PSU if I were you... on a budget you can get away with a Corsair CXM model, if you're not Corsair TXM or RM series, Seasonic Focus Plus, Superflower Leadex III.... a 550W(you can get the 650W too for future upgrades) from any of the models listed above will be plenty for your system.
The alternative would be to just run with the thermaltake until you're saving up for a new PSU... not the optimal strategy, but if you have no other choice...
About that 8 pin PCIe... you just need to plug it in your RX 580, that's it. Also make sure that you uninstall...