If the positioning of the lighting is what you want with the Speedlite on the camera and the other strobe elsewhere, you can get them to fire properly. You need to have BOTH the camera and the Speedlite in fully manual mode. No automation will function properly for the exposure - period.
The reason is fairly simple.
One scenario is that the remote strobe is triggering off the pre-flash from the Speedlite and not recycling fast enough to trigger with the main flash. Thus the remote flash would not contribute to the exposure.
The other possibility for problems is a little more complex. The camera and Speedlite work in concert with each other to determine how to fire the Speedlite for a proper exposure. The Speedlite emits a pre-flash which the camera analyses. The camera then tells the Speedlite how long a burst to emit as well as controlling its own aperture and shutter speed. If you got a remote flash to pop at the same time as the main flash, you would definitely have an overexposure situation unless the remote flash is merely illuminating otherwise dark background or something like that. The reason is that when analysing the pre-flash, the camera knew nothing about the extra flash source and could not possibly adjust things for it.
Does this make sense?