This is intended behavior, I am sure. I assume that this happens when you copy text from Writer to Writer.
Any character formatting which has been applied (by text style or direct formatting) to the text you copy, will carry over to the target. Formatting based on paragraph style (i.e. not explicitly applied to the text you copied) does not carry over to the target.
In other words: Target paragraph style also applies to new text pasted when that text does not carry explicit formatting.
When you copy from other applications which do not use a compatible system of styles, the formatting should carry over in most cases.
Try the suggestion in this document where some words have been explicitly formatted to the same settings as the style already applies. The suggested copy/paste operation may be revealing...