How does something like that plug into a common smartphone?
They don't.
The antenna feeds a bi-directional amplifier (BDA) located in the vehicle. The BDA re-radiates the signal inside the cabin.
They can work well if designed well, installed correctly, and used correctly.
If not, they cause interference, don't work, make things worse, etc.
Many years ago I had one in a truck. The BDA portion was built into a cradle that held the phone. The BDA was powered off 12 volts switched by ignition. I mounted an NMO mount on the roof and had a small blade style cellular antenna. Worked really well out in the boonies. Would take a marginal signal and boost it to the point that getting phone calls, text messages and data in/out was possible.