My mother is overbearing and my father is not (parents are divorced) but even after 8 plus years away from home they both still have emergency contact info for me (I'm 26). And I don't think that request itself is unreasonable. Emergency info is not just for when something happens to you but also for instances where they need to get ahold of you suddenly (example, one of them is in the hospital). If you're someone who is away from your phone for several hour stretches it makes sense for them to have some way of getting ahold of you. I also don't think their reaction was too extreme. You both screwed up here. However your fuck up was just out of forgetfulness and theirs was out of worry and concern, so I do think you can afford to cut them some slack.

You're an adult, if you say you're going to call someone when you get home do it. Surely you can set a reminder on your phone to send a text. If you don't feel comfortable doing that or capable of remembering to do so, don't promise to do so. They are concerned about you so while it may seem like they overreacted (and they did) they are hardly acting in abusive ways (at least as far as worrying for your safety and being upset that you failed to call them). As far as I can tell they reasonably expected to hear from you about six hours later than you said they'd hear from you and you know they worry/ have some anxiety issues. So this wasn't two seconds as you say. Six hours is a lot of time for people to sit around waiting and fear the worst. If anything it is a testament to the fact that they think you're more likely to be in an accident than just fucking around so that speaks to your responsibility. You kind of were being inconsiderate. To some generations a phone call is much more similar to a serious commitment. If you had a date and the person showed up six hours later than planned without any contact I bet you'd be concerned about their safety too. What you wrote here does kind of make you sound like a petulant child. If you actually don't want a cell phone don't have one, problem solved.

If you set healthy boundaries with them do you think they are capable of following them? It sounds like the bigger problem here is that you either go along with what they want to avoid a fight but don't take their wants seriously (which is really passive aggressive) or you get angry at them without trying to understand the rationale behind their overbearing behavior. Are all of you capable of having a calm discussion about this where you all get to hear each other's points of view? For example, when everything has calmed down, could you say "given what happened the other day I'm concerned you'll misuse any numbers I give you and I want to ensure my roommates' time and boundaries are respected. I felt that you called way more times than the situation warranted, However in case of emergency, here is roommate XYZs email address and cell. If I do not respond for over 24 hours you have my permission to email him or her (ccing me) and if you don't hear back from either of us for over four hours you then may follow up with a phone call. If you aren't capable of reasonably complying with this request I will ask that they block your numbers and email addresses." Then talk to your roommate and have that person alert you if your parents do act inappropriately.

Where your parents did act in really inappropriate ways was by threatening to take away your support. That said, it would piss me off too if I were paying for someone's cell phone bill and they failed to call when they said they would. I think if you want to live like an adult with your own boundaries and rules you need to stop relying on their support, especially if you know that they are going to threaten to take it away. Get your own cell phone plan. Look into going on your schools health insurance plan (if that isn't an option remember that your parents love you and are, if anything, extremely worried about your safety so the chances that they take away your healthcare coverage are minuscule). If you don't want to do that try to have a discussion with them about why threatening you isn't healthy for anyone.

Regardless, I think giving them some sort of way to get in touch with you in case of an emergency is perfectly reasonable.