Yes, I agree with John..It sounds unusual. There are also chances that the developers use the same name for the data items(Stop After Items, Stop ASAP, and Stop After Time) , but give hard coded values in the data item making it as a Number/Text/Datetime. It depends on how you give values to this process.
Session variables are used only when the Control Room has to change a value during the runtime. And for eg, if a process needs to stop by 8AM EST, we would directly give the Stop After Time as 8 AM by making it as a DateTime data item instead of a session variable.