Many people it does seem do not like getting auto replies when it comes to email, well twitter is no different there is a growing number of people it does seem who dislike what are called Auto DMs as much if not more so then they dislike auto-reply emails.
I’m in the group that doesn’t like the Auto-DMs but auto-emails those for the most part I don’t have an issue with since it lets me know that so and so did get the email sent to them at least, beyond that its has no impact on me. For myself and many others Auto-DMs is very much impersonal, it doesn’t take long to send a shout out to those who choose to follow you and make what you have to say to them in a short DM sound like you are really pleased that they have chosen to follow you.
But is there ever a time that an Auto-DM is the right things to set up and use? Well for businesses that are promoting something it might well be a good way for their new followers to get a link or something of a promotional offer (free X or Y type deal for a thank you for them for following you type deal). But for the average user I do not think having an auto DM active is a good idea what so ever (less you are going on vacation and wish to let any new followers know that you are away so wont me tweeting for X period of time, then I can see it as a good option).
So to me the short of it all is that Auto DM is something that should only be used under certain circumstances other wise it should be left well enough alone.