Most systems are just taking the calls to the company number and forwarding them directly to you. The only charge I can see you incurring would be using up your minutes if you don't have an unlimited plan.
Although forwarding calls to your personal number is a rather janky way of going about it, and can be incredibly annoying if the forwarding isn't turned off when you're not on-shift, or when you're done working for them. Might be a good idea to setup a Google Voice number or something, let them have THAT one, and just be logged in on your computer with a headset on. Then when you log out, you know you won't be getting calls when you're not supposed to be.
And if you want to be super cautious, make sure all your passwords on your personal account are set properly, and contact your provider about a "port-out" block, which prevents your number from being changed to another provider without you specifically calling to authorize it. IIRC, most providers can do this, but it's been a while since I worked for one.
Honestly, if they want to forward calls to your phone instead of provide you with a phone to use, they might be more hassle than they're worth.