I'd explain it to people in a more general sense. Tell them you're not someone who carries your phone with you at all times and you're not instantly contactable in general, that sometimes you switch it off completely for an extended period of time to take some space and there's no need to worry when you do this. If people are taking it personally after that, they're an arsehole.
Their need to reassure themselves that you're still alive doesn't trump your need for some space. You're allowed to centre yourself in your own life. If you've warned them in advance that it's part of your personality/normal behaviour for you, then they should accept it. If they can't accept it, they need to end the relationship between you and not have any contact with you at all. What they can't do is start telling you how you must behave, that's your choice not theirs.
Same goes for answering the door if they show up uninvited, having been unable to get you on the phone. It doesn't matter if you're home, it doesn't matter if they know you're home, if you don't feel like talking to anyone you don't have to answer the door.
If you wanted to you could re-record your voicemail before switching off the phone, to say "I'm taking a break from socialising right now, drop me an email if you want and I'll get back to you when I'm ready". That way anyone genuinely concerned about your health and wellbeing has a way of raising that and getting reassured at a later date. Don't feel you have to do this though, if you don't want to.