Sought some clarity on this and got a very quick reply that caused an update to the tournament rules...
When counting for weak-side-wins, do timed win and timed ties count? From the current wording of the Tournament document I would say no but I wanted to check and make sure I am reading it right.
"If time is called and neither player has achieved victory in the current game, then play continues until both players have completed one turn. If victory has still not been achieved after the final turn, then no one wins the game and the player with the highest number of agenda points gains 1 prestige. If players have the same number of agenda points, they each gain 1 prestige."
Thanks for the quesiton. Timed wins are wins, and so they do count for weak-side-wins. We released an update to the tournament rules (1.4.1) that makes this more explicit:Android Netrunner Tournament Rules
"If victory has still not been achieved after the final turn, then the player with the highest number of agenda points gets a modified win and gains 1 prestige."