What format are the videos you are trying to import? Where did they originate from? If you take a test recording using Camtasia (say, of a YouTube video) then import that into a new project, do you have the sync issue?
I had something similar happen in Camtasia, where is played fine in preview, but when I published it there was significant lag time between the audio and video. I had to make sure that the SCORM box was checked and then it worked fine.