As long as you’ve covered the basics—dates of your absence and who to contact in your absence—you should be good to go.
I give my folks scripts because, otherwise, I end up with long winding OOOs that talk about why they’re out but not what the writer/caller should do to get help (staff is 1/3 entry-level with varying degrees of professional office familiarity). I do not have the time to micromanage to this level, though – if I see an off-spec OOO, I send the how-to guide and remind them that they need to tell people who to call while they’re out or to mention the specific dates, but most of them have good judgment enough not to be totally inappropriate to the point I need IT to intervene.

A ‘Type A’ who can’t ever fully switch-off from work… at least they’re honest about it!
I have a colleague who directs people to email an alternative email alias when she’s on leave. This alternative email alias? Yup goes to her. Don’t know why she does it. She’s also set a rule in her team that they have to answer each others’ phones of someone is away from their desk. Inevitably, the person answering the phone can’t help and tells the caller to send an email. It drives me up the wall.