Blizz has said there's a catch up mechanic of some sort, but I'm not sure what their plan is for implementation.

A guildie posted this handy info in Discord:

"Sounds like the best course of action is to save all of your Vessel of Horrific Visions and only use them to rank up your cloak as the cap goes up. This will allow you to upgrade your cloak to the next rank as the cap is raised on Tuesday rather than having to wait and collect the jars needed throughout the week. Additionally, by the time we get to Week 9, you'll be able to unlock Rank 14 on Tuesday reset by popping all of your saved Vessels. People who didn't save at all will be stuck here for 2 full weeks (6 runs minimum). This means you could be 1-2 weeks ahead of people to get Rank 15 and permanently ahead when it comes to weekly corruption resist (compared to people who didn't save). Edit: That would look like this:

• Week 1: 2 free upgrades & use 3 jars (rank 6)
• Week 2: use 1 jar (rank 7), +2 saved (2 total)
• Week 3: use 1 jar (rank 8), +3 saved (4 total)
• Week 4: use 2 jars (rank 9), +3 saved (5 total)
• Week 5: use 2 jars (rank 10), +3 saved (6 total)
• Week 6: use 3 jars (rank 11), +3 saved (6 total)
• Week 7: use 1 jar (rank 12), +3 saved (8 total)
• Week 8: use 3 jars (rank 13), +3 saved (8 total)
• Week 9: use 6 jars (rank 14), +3 saved (5 total)
• Week 10+ use 5 jars and keep using jars as you get them until rank 15

TLDR You should probably only use the minimum number Vessels required to upgrade your cloak each week. But you should still farm out the 3 per week and save what you don't use."