Yup, something wrong somewhere. I am a NOTORIOUSLY difficult person to please, especially when it comes to tuners, and I have found that the axe is much to my liking. There are some issues when tuning basses and 7-9string instruments, but otherwise, it is a very smooth, very accurate tuner. What tuning are you tuning to? Do you have the tone pot rolled back? Is the guitar volume all the way up? Are there any other pedals etc in your chain? Do you have good cables?
Also note that the initial transients of a note will send the string slightly sharp, whether you hit hard or not, but is much more prominent if you hit hard. Some tuners do not pick up this transient, but the axe does. It could be this that you are seeing as well. It's best to wait a second for the initial attack to die off before making tuning adjustments.