The primary cause of changing tension as it goes around has been jamming of the chain due to worn pins/rollers. As the chain starts to wear from lack of lubrication/over tightening/ impaction of contaminate a few links will be contaminated worse then the others and will jam instead of bending smoothly as they engage the sprockets. the problem can be abated temporarily with a very thorough cleaning and re-lubrication, the worse the chain is the quicker the problem will return.
ALWAYS (yes ALWAYS) replace both sprockets when you replace the chain if you want to get maximum life from a chain. Even a tenth of a mm of wear (0.004") will quickly be transferred from the worn sprockets into the chain.
If you can check the sprocket alignment should be parallel to each other and within a millimeter or so of aligned. A taught wire will work, a laser if you know how to align the beam to the sprockets.
I know they draw more power and on some machines cannot be used because if interference problems, but I do not hesitate to recommend an O-ring chain. it keeps the pin/roller sealed from outside contamination and will run smoother/longer with minimal maintenance. Particularly effective in dusty environments. You still must clean the O-ring chain well with WD40 or similar, wipe ti down till dry and let the cleaner flash off, then use a good minimal fling lubricant. This lube application is primarily for the leaf surfaces as the O-rings prevent new lubricant from entering the pin/roller area.
Just to brag a little...My Diamond Nickle plated O-ring chain has 8000 miles and has stretched/worn less then 1 notch on the alignment marks.