Time travel in Primeval is rather simple: time-portals, known as anomalies, mysteriously open in unforeseen moments and locations, connecting the present with random times, past and future.. There are some creatures and characters that come and go and get trapped in different times that are not their own. So we only need to try to follow the changes that come about when time-travel to the past takes place. So for example, when Emily arrives in the present from Victorian London, nothing is problematic until she goes back to her past with knowledge gained in the present (her future) and a rogue creature ends up thee as well (seasons 4 and 5). If we were to go with a previous case where changes were made to the past, to be consistent within the Primeval universe the present would have had to change, even though Emily and the creature are brought back to our present again. In season 2, two baby creatures from the future end up left in prehistoric times, and strangely this affected the present in some strange ways: the team is now a separate research institution, the ARC , but their individual lives remain unchanged, while Claudia Brown disappears completely but the same woman appears again coincidentally connected to the ARC as a PR person with the name Jenny Lewis.
In the changes that happened in season 2, to be fully consistent, no one should have remembered the "original" timeline, but for the plot it was necessary that one of the team did, in order to maintain the love story arc between Nick Cutter and Claudia/Jenny. To be fully consistent and eliminate the paradox, what we had seen so far would have bee either just a conjecture "what could have been", plus the time-travelers would have had to meet the "new" selves in the present, not "be" themselves again in the changed timeline. (Another way to avoid the paradox would have been for them to disappear from existence the very moment they attempted to travel to the past, but then there would be no show...).
There is also debate on whether the "duplicate" Matt we see in the very last scene of the last chapter is a future self that has somehow come to the present (e.g. to warn him that the end of the world has not been avoided after all) or a hallucination. Since the show will not continue, we will never know...
More on Primeval's timeline: http://primeval.wikia.com/wiki/Timeline