This is how I fixed it:
In Launchbox go to Tools->Manage Emulators. Click edit on your ePSXe. Put this in the AutoHotKey Script:
; This section closes EPSXE when pressing alt+f4(the auto close for controller)
$!f4::
{
Process, Close, {{{StartupEXE}}}
}
The automation close via controller calls ALT+F4 on the keyboard to close the emu. So by using an AutoHotKey Script to close the application on ALT+F4 it solves the problem. This should work with any other emulators that experience this issue(epsxe is the only one I found)