I have made live bets on a few bitcoin sports betting sites including Nitrogensports, Directbet and Cloudbet and a few fiat bookmakers as well in the past. As far as I know, the result of a live handicap bet is always determined by the result since the start of the game, but not only by the result since you make the bet.
Well I don't know where you have been betting, for live handicap betting it is always on the remainder of the match. A quick google also confirms that:
I can list alot more but you get the idea.