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If I was writing a fiction and felt the need to address this, I would make it so where you wind up is based on the location of the time machine in the time you travel. But also I probably wouldn't and just handwave it
A time machine, at its very very core, is a literary device. You wouldn't bring up this nuance unless it was important to the plot of the story.
It's like warp drives. The point of warp or any FTL travel is to skip the boring parts. You only learn about warp drives when something goes wrong.
Teleporters as well.
I remember having access to one in an RPG (rogue trader, teleportarium), and almost every session was "why can't we use the teleporter for this?". Eventually we made a rule that we could only use it once per session, which meant functionally we saved it for emergencies or something really funny.
There is an enjoyment to solving problems in the engineering sense, but in an oppositional sense you dont really tell any stories other than about how you solved a puzzle you yourself invented