The kills listed under each Hero on the leader selection screen is their top score (highest kills in one game) and is not a cumulative total number of kills. Unless you beat your previous top score with that Hero, this number will not increase. The kills towards earning the next star do continue to accumulate as you play regardless of the top score.
To see how many more kills are needed to level up a hero, tap on the +star button next to a hero's star count. This will list the number of gems to upgrade. The number of kills remaining to level up is half this amount.