Well, I bid on a domain with 2 ids (actually, I was confused as it was my first time). The id with which I bid first won it.
Well, I don't think there is any sign for the person who bid first. So, it might be better to bid on to win it on the last minutes.
Green tick is for both bidders.
Unless until the bidding time expires and no one increases their bid, you might not be able to know who bid first.