What would be those observations and reasoning? It'd be good to know if something is in fact taking somewhere in the range of a day or so to start-up/initiate.
You look at the way animations unfold. If they have a slight pause before starting the background task was already running. If they stutter, the animation has triggered the task. If they pause near the end the task was started but not related to the animation. Lots of tasks create a slight slow motion in animations. If the phone is slightly warm and keeps its temperature while using the app you are dealing with background cpu usage. If it heats up periodically it's the app's fault. If I remember more I'll write them. But I pick up these things subliminally, after using many types of electronics