No it starts counting when you can access the event in this case at lvl 30. They would have to add a new background counter for that and that isn't really a priority for early game players. Unfortuantly between the effort of adding such a feature and how niche the benefit is it may never happen. (that and having access to the event is technically a reward for your effort which gives you an additional benefit for effort/recharge)

That aside I don't get the Mei hate, is this because of the overwatch character? cuz this was totally expected since fireworks primarily has dealt with event nin freebies. I for one know that it will in no way negatively impact our clusters race to 4k day 1, etc. and I doubt any ninja will really cause a boycott of the event except suit sasuke, or one of the cat ninja.