Keep an Access Log
If you just go back in time to delete the data you no longer need, then you will keep yourself from being able to use it in the past when you needed it. So instead of deleting it from the whole timeline, you just delete it from most of the timeline.
As the name implies, an access log is a file or data table of some sort that you associate with data to keep a record of every time the data was accessed. So, let's say you have a user record that has been accessed 7 times in the past 5 years since it was created, you now know the exact 7 moments in time you need this data to be there. So, using the log file you just delete everything around those 7 moments (including the log record itself), so that way if a time hacker tried to go back in time to access the record, he could not without knowing the exact microsecond that this information will pop in and out of existence... which he can't know because the only place to look that information up is in these 7 microseconds spread out across the 5 years this data existed. This means any random scan of the hard drive in the past would only have a 2.3e13 to 1 chance of having the data on it.
Furthermore, while this technology makes data breaches seem more dangerous, they actually make them less dangerous than they are in our world. In our world, hacks and spyware are nearly always identified and addressed eventually, but the damage that is done in the past in immutable. However, in your world, if you ever find malware on your server you not only have the power to delete it, but you can delete the malware from every point in history such that the data was never compromised and hackers who get caught don't just get locked out, but they lose everything they ever gained from thier hack. Not getting caught for now is a lot easier to do as a hacker than not getting caught ever.
Reality Check
Most people have access to negative mass tachyons if they are middle class or higher.
I find this a very unlikely event at any point in the future no matter how advanced society becomes. Today, nuclear weapons are a nearly 80 year old technology that are disturbingly easy to make with modern manufacturing technologies compared to all the smart phones, nanotechnologies, and other high-end capabilities our society has access to. But the average middle class citizen can not nor will he ever be given the freedom to own nuclear weapons because that is automatic suicide for your entire civilization, and probably the world.
The ability to go back in time and edit it, is FAR more dangerous than any nuke. While a nuke can end a civilization, a rando with a gun could go back in time to prevent a civilization from ever being born causing far more damage with far less resources; so, for this setting to make any since, the technology to edit data in the past (pushing around a couple of electrons here and there) has to be distinctly different than being able to actually send a person into the past, and even the ability to manipulate past records would have to be VERY strictly regulated or preventable. If the same technology that a private citizen can use to protect thier privacy could also be used to manipulate the outcome of the 45th presidential election of the United States, then the benefits would outweigh the risk of allowing private ownership, and all time travel would become the exclusive prevue of a small number of superpower governments.
So to limit the destructive eventuality of these devices, there would need to be one of 2 solutions. Either:
A) An effective means of locking off significant parts of the timeline to time travel... unfortunately, making this whole technology a moot point. Or B) This technology needs to be a closely guarded secrete controlled only by a small handful of individuals to make sure no sociopath ever gets ahold of it and decides to start playing God over billions of people's lives.