How am I alerted by the 4S - via my phone or via the base unit?
Base unit that you carry with you.
The 4S is built in 2 pieces.
Piece 1: You leave at the smoker and has the probes that you put into your meat and/or set on the smoker rack. This way you can measure both meat and get an accurate smoker temp reading at rack level where the meat is. This piece broadcasts signal to Piece 2 which is like a receiver and control unit
Piece 2: Is a Receiver and Control unit. It picks up the broadcast of information from Piece 1. Also you punch in your various alarms and other settings to manage control based on each probe.
Minimally you run 1 one probe at the "Oven" setting so you can set a High and Low value for the alarm to alert you. Should things get too hot or the smoker shut off this thing will save you.
Next probe setting will be a meat setting. I always run mine on custom settings but they have factory ones for chicken, pork, etc. to try and help out. Those are pretty much useless so you just override to your own personal temp values and the alarm for that probe will go off when the temp is hit. Pretty easy.
Now the Bluetooth specification is designed for about 30ft (10meters/yards) of range and Wifi range isn't much better. So bluetooth and wifi units that work with your phone may not be an option unless they can easily and reliably cover the distance you need.
Wifi units can be assisted with wifi extenders that may reach your smoker but that means buying more stuff. Once connected to wifi you can monitor anywhere your phone has connection to your home wifi signal but I'm not sure these devices open up to the internet so you can check anywhere your phone has cell network + internet access. Your home network vs internet network are 2 different animals, especially with access and security.
The 4S has a dedicated radio frequency design so I believe you can get 300ft(100meters/yards) of range out of it. In reality you should always be within 30 seconds to getting to your smoker should a grease fire start or the unit shut down. Burning down the house/apt or starting a county wide grass fire (many places in drought) is not something any of us would enjoy and is easily preventable just by being around to handle it when it starts :)
Always take this into consideration when choosing a remote digital thermometer :)