I get the usefulness of warnings for fanfic and personal accounts on a blog. But magazines and anthologies provide a context: if a story doesn't fit the editor's agenda, why is it being published there? You should know that you'll find an Apex story at Apex, just as you'll get a Disney story from Disney.
I can't imagine a warning that doesn't weaken the first-timer's experience. Googling "Lynne Thomas Apex Magazine Trigger Warning", I came on someone's link-sharing that included this description:
[TRIGGER WARNING: Domestic Violence.] What I like best about this story is that it starts out in an unexpected way given what’s really going on (which you understand at the end).The person giving the warning has told you to watch for something that the writer hoped would surprise you.
If I was starting a magazine right now, I would call it Trigger Warning.