Network configuration question?

I need the following question answered.

When two subnets share the same physical cable, are there security issues with the one subnet being able to get to the second subnet? For example, at our co-location facility, we have a switch that the WAN Internet connection comes into. We are considering also running our 10.0.0.X network through the NIC, same cable and same switch. Will doing so expose our internal (10.0.0.X) network to the internet?

Thanks in advance!