Last week I heard this on a podcast, can't remember which one. Apparently, most people use ASAP with the wrong meaning in mind.
As soon as is possible; at one's earliest convenience; at the earliest possible time.
source: https://en.wiktionary.org/wiki/as_soon_as_possible
It doesn't mean you need to drop everything the moment someone puts ASAP at the end of their message. It has a literal meaning: do it when you're next able to. On your terms, not the sender's.