The harder stance, is that since the person from the past, returns to the past, they create the future they then interact with, by the actions they undertake after returning to the past.
This ensures that the future that they get taken to is always the same future, and the actions taken are always the same. Similar in nature to a closed timelike curve.
EG-- Person A), from the future, travels back in time to collect person B). Person B) then goes on an adventure with Person A), in the future. Person B) then gets returned to their normal life in the past. This is NOT the end of person B) though. They continue to exist, and make choices-- now armed with knowledge of the future. The actions they undertake will unerringly cause the future in which Person A) is born, raised, and learns about person B) from history, compelling person A) to go back in time, and collect person B), to have the adventure. The timeline is closed, and timelike, hence "closed timelike curve" Actions caused by B) in the past, induce the creation of A), and the events that shape A)'s history, compelling A) to interact with B), which then influences B), compelling B) to create the future that A) is from. [loop]...[loop]...[loop]... Time continues normally on either side of the curve, but where the past and future met, the closed timelike structure is stable, but not-normal. There is no discernible way to determine how it was created initially.