I saved my 2nd batch of WG weekly quests and did them Monday night around 10pm to test if they get reset regardless of the 4 day timer on Tuesday morning. The result? They were reset at 3am along with the rest of the dailies.
I play on US Ner'zhul which is in PDT time, this week we did not have the weekly maintenance, not even a server restart, I also did the 2ed batch of quests Monday morning.
Shown in the screenshots below, the quests has been reset some time between 9:06AM PDT and 10:14AM PDT on Tuseday
so every tuesday and saturday i presume for US and wed and sun for EU ?
Seems more complicated then that, this is what I have for this week:
Siege quest: 9/1 16:17
Slay then all!: 9/1 16:17
Victory in Wintergrasp: 9/1 16:17
Gathering quest: 9/1 22:33
Toppling the Towers: 9/3 04:21
But as of 9/6 09:13 I still can't accept the 2ed round of quests this week.
Edit: Server: US Ner'zhul, PDT time zone
Logged off 9/6 17:36 when I still couldn't accept any quests
Logged back in 9/6 22:50 we had WG and I could accept Siege quest, Slay then all!, Gathering quest. So it must have reset sometime between. I assume Victory in Wintergrasp has also reset, but this quest is only available during battle. I will see if I can accept Toppling the Towers in 1 hour, my guess is it hasn't reset.
9/7 00:01 Victory in Wintergrasp is available as I thought, and Toppling the Towers was not.
9/7 10:01 Toppling the Towers still hasn't reset for me.
9/8 01:06 Last WG defense until 3am maintenance, still no Toppling the Towers, that means if you complete wg quests on after thursday, you only get to do them once that week.
I do them twice every week for a few months already. My experience is there are 2 reset triggers.
1. They reset every Tuesday 3am server time, same time as daily resets, for US servers.
2. They reset 4 days after you turn in the quest, with each quest on a different timer.