I’ve never really paid much attention to or trusted presence status, with the exception of statuses that are manually set (e.g. do not disturb in Slack and similar).
It’s kind of funny, considering that presence is probably the most challenging technical requirement for large-scale messaging platforms. I will say that my two most-used messaging platforms, iMessage and Slack, both usually do a great job of delivering push notifications to only the ideal device (my phone, tablet, or computer). My intuition is that this logic is roughly the same as presence.