The problem is not the proxy because when you export it uses the original video, not the proxy. So, the problem is with the original. Since the proxy is not the original, using them can mask a problem with the original. What made the original videos? Are they variable frame rate? If you think there is a problem (you can test it alone outside of the project) then you might need to convert the original using Properties > Convert.
Sometimes, when using proxy, you need to turn if off during a review of everything before export.