It's still your move, you still have a move to make. In the meantime, your opponent can think about your draw offer, but that doesn't stop your clock (because you would get free time if you knew your opponent wasn't going to accept anyway).
If he makes a move without accepting, then it counts as a refusal, but it's perfectly normal for him to wait for your move to decide whether he's going to accept or not.
Therefore it's customary to make your move, then make a draw offer. Don't make a draw offer before you make your move as the opponent will just wait for your move anyway.
G'day
I have a very close game on at the moment, in fact i just clicked the "offer draw" button.
1. the game still shows as "my move" (so do i assume my opponant turned the offer down)?
2. there is a comment that says "draw offer pending" (not a player comment), which made me think my opponant had to respond re accepting the draw or not ... and yet my time is still running down.
Does this all sound right?