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Time and space are the same thing, if you’re traveling in time it seems like you could travel in space at the same time.
Since relativity tells us there is no universal reference frame, then it having its reference tied to earth is perfectly valid.
Also sidenote: my favourite idea about time travel is that time travel is entirely possible, but will never be invented, because the timeline where its not invented is the only stable timeline. Because any timeline where it IS invented gets changed as soon as you use it, meaning the timeline changes over and over again every time time travel is invented repeatedly either infinitely or until someone accidentally creates a timeline where its never invented, only then does the timeline stop changing and we can actually experience it. So because we exist and can experience time, we can deduce that we will never invent time travel.
There can be stable timelines with time travel - there’s actually 3 states:
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Perpetual instability, where the timeline changes each time the time machine is used but never reaches the same state twice
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Perpetual cyclic stability, where people’s actions in modifying the timeline lead to it eventually reaching the same state, eg. you go back in time to kill someone who becomes evil and oppresses you but the near death experience leads them capture you, so you can’t time travel any more, and to blame your people and start oppressing them, leading to the same actions
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Stability without time travel, which is the default state but incredibly hard to get once time travel is invented as with nobody to stop time travel being invented it would probably get invented again, however parts of a cyclically stable timeline could have nobody having access to time travel, but any actions by time travellers to stop time travel would likely lead to the second rather than third option
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