I wondered that, deleting the cache in the panel in Blender, the problem is solved and the particles or the smoke start correctly around the Flow object.
So, I think that this is non a friendly method.
It's OK to remove the Bake buttons and the real time simulations, but maybe you can add a "RESET CACHE" button?
Thanx!
Andrea

I can attach a blend file but I see what he is saying, and it is not related to Gas domains only - it also affects liquid domains. Here's what happens and I can replicate it 100% on 2.83 as of current build:

1. Create a liquid domain and an inflow object within it. Ensure the cache type is set to Replay.
2. Set the domain to show as wireframe in the viewport so you can see the particles within it.
3. Play 20-30 frames and observe particles behaving properly.
4. Move the domain down on the Z axis while keeping the inflow object within it.
5. Rewind to frame 1 and play again. Note that the fluid positions are still cached and calculated relative to the original domain position.
6. The only way to fix it is to set cache type to Final, start baking, then free all data, then go back to Replay cache type.

Some button or option to clear the replay cache is what OP is asking for, and I think that's a reasonable request. Or, the replay cache should reset at the start of playback at frame 1 if changes to the domain transform have occurred.

Currently, fiddling with domain settings and changing them back does force a cache reset, but that's not a clean way to handle this use case.

Correct Nikhil.
I think that includIng into the final version 2.83 a reset button for the chache or force anyway the chache to reset automatically when restart the animation is a very reasonable solution.
Waiting.
Thank you

I wanted to tag @Sebastián Barschkis (sebbas) so he saw this, as he is one of the super-smart physics brains here! 😀

Sebastián,

Take a quick look at my comment above with steps to reproduce and I think you'll see right away what we are talking about.