Eight 10W lights is 80 W. That is 6.67 A. If you are running both sets at the same time, you are either overloading the power supply or the lights aren't taking their rated current.
If the power supply is a switch-mode one, it will have a current limit in it so fuses wouldn't protect anything. The danger with a short when you have a power supply like that is that the output voltage will reduce, and it could be the that a MOSFET doesn't turn on completely, and gets really hot. However, if they are pre-built MOSFET circuits then they may have protection against that.