Apparently Wells didn't know exactly how time travel would work and either A. planned on taking Barry's place as Flash in this timeline or B. being Flash in the future. His real motives don't make a lot of sense no matter what they are really, but that's the comics for ya.
Also, it seems that in this series to travel in time is to physically travel there with your body intact. In that case (and most if you think about it in fiction) you can be in two places at the same time at different ages. Now the question is, why didn't Barry stick around and stop Wells back then or help himself out later on? Maybe Barry is much more responsible with the timeline than Wells is due to circumstances his choices make when time travelling (like this episode).