Numbers Copy Paste Not Workings as Expected

I can't reproduce this, which implies there's something about how you're doing this that's making a difference.

First up, realize that Numbers has a couple of different ways of pasting, depending on a) what's on the clipboard, and b) what you have selected when you paste.

Let's start with what you're copying - are you selecting an entire row (or series of rows) by clicking in the Row Numbers? Or are you copying cells (even if all the cells in a row) by clicking and dragging or shift-clicking.

The difference is subtle, but may be important.

For comparison, here's where I selected a row by clicking in the Row Number in the margin:

And here's where I selected a range of cells by clicking on cell A2 and dragging across the columns:

The only significant difference is in how the Row Number is highlighted.

So how are you copying the data?

Secondly, Numbers acts differently depending on what's selected when you paste into the other sheet.

If nothing is selected, the Numbers creates a new table with that data.

If a cell is selected, then Numbers pastes the data at that cell, maintaining the same relative offsets for the data (e.g. if I copy row 2 from the table above and paste into another sheet when cell D4 is active, then D4 will take the first copied cell's value ("Jones, K"), while E4 will take 'Manager', F4 gets $35, etc.

If a cell is ACTIVE (e.g. you double-clicked on the cell as if to type a value) then the copied values will be pasted as a single text string in the cell.

None of the above match your experience relating to the double-header, but it's still worth clarifying quite how you're copying the data to see if anything stands out.