The contact will go through the automation that Sunday or that day (the 14th). It will not wait for the next Sunday or until the following 14th of the month.
Hope that clears everything up, but reach out if you have any other questions.
Similar question… If my automation is 4 days long and a prospect enters on day 2 at 11am AND I have a wait until 7am to do the next action I have noticed a queue backlog buildup. How do I get those who enter AFTER the wait until 7am time to move to the action, which is send an email.
If you don’t want anyone to get stuck at the 7am wait step you could do something similar to this: http://screen.ac/2N2A3w1n2g0x
That’ll push them through, but it’ll be anytime after that. If you have a set time limit, you could combine “greater than or equal to 7 AND less than or equal to 12pm” for example.
Otherwise a goal/tag system would be better if you don’t want previous day emails to go out. For this it would be best to reach out to support for more dedicated solution based on the requirements.