No need to concern yourself about minor temperature fluctuations or difference in readings between the two temp probes.
These smokers all have a range of plus/minus in relation to the temperature setting you choose. These swings will not affect cooking times to any noticeable degree. In a way the swings cancel one another out.
If you are getting into more detailed smoking such as sausage temperature control is more critical and a PID can be utilized to maintain steady temperature settings.
The difference in temperature readings between the factory sensor and your aftermarket one is possibly due to probe location within the smoker. There are substantial temperature differences within the cabinet areas due to many factors including vent position, outside temperature, type and amount of product placed within . Generally the upper rack areas are somewhat cooler than the lower racks.
Nothing you have described is unusual or going to affect your product unless you are doing temperature sensitive things like sausage.