As soon as he emerged out of the Speed Force, BAM! Erased from existence. Without Eddie Thawne, there IS No Reverse Flash, Paradox or not. Period. It was a very weak explanation by the writers and I'm not buying it for a second.
That leaves only two options that can explain this.
1. Eddie Thawne was somehow revived and is alive.
2. From dialogue in the show, we know that they are all living in an alternate reality because in the original, Barry becomes the Flash a bit later and Nora never dies. But by going back in time and killing Nora, taking over Dr. Wells' life, building the particle accelerator so Barry becomes the Flash sooner so Thawne can go home sooner, etc, this created an alternate timeline to the main timeline. And the Reverse Flash we saw is from the MAIN timeline and in the MAIN timeline, Eddie Thawne is still alive because he never killed himself.
But the Reverse Flash accidentally traveled to the alternate timeline somehow when he wasn't supposed to and learned some key things that will allow him to become his alternate self, but for now he is still from the MAIN timeline because his alternate self is erased.
I don't think we need to address the Eobard Thawne RF erasure from time. The RF in season 2 is Dr. Stein from Earth 2. At 2 different points (when 1st arriving at/in Earth Prime and after watching Flash disable the rigged 18 wheeler) Gideon refers to this RF as "Dr. Stein." Therefore, this RF is from a different dimension and the erasure of Eobard Thawne from Earth Prime timeline does not affect him.
What do you think Knight?