In my opinion, it is not normal for cigars to burn unevenly. If my cigars burn unevenly, then it is usually either an error I made while lighting the cigar or a problem with my humidity. If a cigar burns down one side, it could be because some of the tobacco inside is not evenly humidified. Some of the leaves maybe more dry than others and that will cause an uneven burn. I would check your humidor and make sure your humidity is between 68 and 72 percent, in addition, I would also rotate the cigars on a regular basis to be sure the humidity is evenly distributed throughout all of your sticks.
"Tobacco is the plant that converts thoughts into dreams." -Victor Hugo-