The short version
The official description says your pets earn money while you are away. To estimate it safely, observe your current income over a short measured period, convert that result to cash per minute, and multiply it by the minutes you plan to be offline. Recheck the actual return before using the same rate again.
Offline earnings connect pet ownership to the next session even when you are not actively raiding or building. That makes away time part of the progression loop, but it does not reveal a universal rate: different pets, updates, caps, or server rules may change the result. The useful tool is a transparent estimate built from your observation.