Since this is here, I'm going to just drop some more data I've been gathering so folks can use it or not as they see fit:
Fresh, as expected, updates pretty much immediately when a new episode is posted.
Popular updates at noon and midnight, PST. (Edited: I accidentally typed EST. That was incorrect. Everything on Tapas is PST)
Dashboard stats for Views and Likes update hourly. Trending appears to update hourly as well, but I haven't 100% verified that yet. Will update when I do. (Edit: Best I can tell, Trending doesn't appear to update hourly with dashboard stat update, but as others have noted, Trending is kinda weird anyway. For example, at the time of this post, Blood Moon is highest on Free To Read Trending in Fantasy. Wrath of the White Wolf is in fourth spot. However, if I switch Trending to include Premium titles, Wrat of the White Wolf jumps to #1 overall, and Blood Moon falls #18. Best guess I have is that one list weights Views/Likes differently than the other, or they update on separate schedules.)
Subscribers and Subscribers Total count is a little weird. I've seen it react immediately to an unsub, but not to a new sub. It may be operating on its own timer or qualifications. That's been the toughest one to test. It will ALWAYS update to current at the top of hour, no matter what, but if it updates before that I'm unsure.
So, with that, if someone wanted to, they could try and figure out the right times of day and days of week for their specific genre to update. It's going to change for everybody and will change based on how many people care enough to change their schedule for someone else. For example, if you've got a really popular title in a popular category and everybody else posts at 3pm PST, you could try for 12pm PST to see if you can get enough Views/Likes off of the Fresh list to rank up on Popular before the big titles post so you have visibility there for longer. In a smaller category, simply having good, reliable material the same 1-3 days a week will probably do plenty for you. After all, none of this is likely to have anything more than a negligible affect on your views unless you're already quite a ways up there in subscribers, and you got that far by having a consistent schedule with quality material.
I don't know if this is helpful for anybody, but without Google Analytics to break stuff down, I got curious (and am working through anxiety of kitty in hospital for emergency scary stuff) so I decided to record the observations I was using to distract myself.