You should cut that out.

You've basically answered the question yourself in describing the situation to us: You have a requirement that characters have a backstory. If they don't bring a backstory, you write a “sadistic” backstory that “affects them badly” and “mock” them with it, and a player has confronted you that they feel bullied. (This is all your own words.) I am relieved you listened to your own alarm bells and asked us. You are being abusive towards your players and need to stop.

Now there's a possibility this is a miscommunication or an English-second-language issue — others have brought up similar concerns and edited the question accordingly — but at minimum I think we can agree that what's happening here is you have players unable to meet part of the requirements at the start of the game, and you're holding this over their head ongoingly in a way that will compromise their enjoyment of the game, and someone's brought up serious concern about it.

At the very least the punishment you're exerting can and should be replaced with supportive measures assisting these players in engaging in the parts of the game you feel they need to engage in. Worse, what you're doing exacerbates the problem you're trying to resolve (I'll get to that shortly).

Managing differences

Each individual has ways they enjoy playing the game, right? Your method of enjoying the game involves players having backstories. Some players' fun doesn't come from having a pre-written backstory, or they find it difficult creating one.

If you want those players in your game anyway, they need your and the group's assistance and support in onboarding into the game process. This means working with them in a way compatible with their playstyle to get what you need out of their backstory defined when you need it. And I emphasize working with them — you should work in their best interests, in good faith, to produce backstory details you're both happy with. They need your support to help them give you the details you need.

They may not be able to produce everything you need right at the start. Some players like myself have a general idea of a backstory and characterisation, but need to actually start playing to work out the rest — we improvise and flesh out our character as we go, rather than doing it all at once at the start. Work with what you can get.

If there's an up-front rule, you need to find an implementation of it that doesn't feel like bullying to anyone. If someone's feeling bullied, that indicates an implementation malfunction, and that we need to step back and fix something if we value their participation in the group at all — even if we felt it was ostensibly advertised or forewarned. (If we don't value their participation we need to politely disinvite them instead of keeping them around in this state.) A player feeling bullied is a social breakdown state, and we need to revise and correct what's going on, including revising what rules might've lead us there. Your group may be able to help you identify how to better implement this rule, but I suggest the above is a solid start — replace the punishing backstory completely with benevolent exploration together.

Aggressive punishments doesn't solve this

What you're doing is aggressively, or passive-aggressively, abusing your players in-game to punish them for not doing something you wanted them to do. In-game retribution doesn't solve out-of-game issues: you need to talk with these people and give them benevolent support, as in the previous section.

Levelling punishment like this is generally seen as abusiveness and bullying. Trying to resolve out-of-game problems with in-game aggression is a pervasive anti-pattern in our hobby. It creates resentment and anger, it means the targeted party isn't having fun, and it sets back your ability to have a fun game where everyone is contributing meaningfully. What good is that for anyone!?

Ironically, like I said, this anti-pattern actually exacerbates the situation. Abusing your players leads to abused gamer syndrome. Abused gamers don't get invested in their characters or the game world, because their character and the world are being leveraged as a means of abuse, and non-investment is their single best defence against that abuse. Since they cannot get invested in their characters or the world, they also don't generally create backstories (let alone detailed ones), because that requires exercising emotional investment they can't afford to have. This makes them more inclined to play amnesiacs or whatnot, and to ignore the backstory you've given them as much as possible. An uninvested player is un-inclined to portray detailed characterization of their characters in any way. Given the backstory you've created to punish the player, why would they want to get at all invested in this character and portray them, if this character sucks and is being used against them?

Further, dictating the nature of a player character is often seen as a thing DMs should not do in D&D: they have control over absolutely everything else in the world, but players generally expect to maintain their sovereignty over defining and expressing their characters how they wish (it's the only thing the player's granted direct control over). If something you're doing as a DM undermines the player's agency to do that, it may be seen as unwelcome. I don't know to what extent your backstories are doing that, but if it is “a lot” you need to step that back and give those players back control.

Help your players have fun or don't invite them

Basically, don't do stuff you could describe as sadistic or make things awful — unless it's genuinely in the spirit of helping your players have fun. (As in, what they consider to be fun.)

When someone tells you what you're doing is bullying, take that seriously as a sign you need to change what you're doing. You've done this here; thank you.

If you don't think you can seriously facilitate people in good faith who don't produce backstories for their characters, and instead think you'll be using these abusive responses against them... don't invite those people to your game. Just have a hard requirement that they either have a backstory or aren't allowed in. Nobody deserves that level of abuse and you're better off sparing them from it.