I was there in late Sept.
If you don't plan on doing the Heavens Gate tour ; nothing will sell out in advance and I would wait.
The Heavens Gate tour does sell out and is handled/sold differently now then in the past so could sell out quicker now.
You do have to be there on time as it is a small tour, they likely will be flexible if late as they were for me.
In 2016 when we went you could not buy them online ; only the regular tickets for the duomo for the full pass you had to book via email correspondence.
I had bought tickets in advance for an 11 AM time slot/tour I believe. We were coming from Florence and the morning did not go as quickly as I thought so we reached Siena past our slotted time.
They were nice about it and booked me on later one.
The afternoon times until 4 PM were all sold out so they changed my tickets to the 4 PM slot for the tour without charging me.
(my exact recollection on the times may be slightly off)
So instead of seeing the duomo first we headed to the Campo Piazza and spend a few hours there, had lunch, etc... before heading back to the duomo for our tour.
We were only there for the day but we had a rental car so the time didn't matter to us.
The tour is really neat and the tiles were exposed when we visited.
The 3 days thing means the pass is good for the Tour but then also gives you 3 days worth of access to all of the other sites in the complex. Baptristy, Duomo, Museums, etc... it does not need to be purchased 3 days in advance. You could buy day off but risk the times being all sold out.