Before:
After:
The example file is a slightly modified version from T74062.
First first frame is still baked incorrectly, but that is a separate issue. It seems wrong to me that any simulation happens at all in the first frame.
As for T74062, I feel like there is confusion about what adaptive time steps is doing. If I understand it correctly, this setting only has an impact of the fluid itself is moving fast, but not if the emitter is moving fast. Maybe you should clarify that (in a tooltip) and in the thread.