Is it possible they billed at 0:00 GMT? (if you're in the continental US, that can be anywhere from 5-8 pm local time)
Also (and I'm guessing you agree with this): When you tell a customer they won't be charged until a certain date, you should probably either (a) know their timezone and adjust the billing date relative to that or (b) know the earliest date that they might get billed in their timezone and quote them that date rather than GMT, or (c) assume they could live anywhere and don't charge them before that date hits in the last possible timezone. Or just don't provide a date at all if you can't get the system to behave predictably.
I did see that auto-renewal must be disabled at least one day before:
"Automatic Renewal: To the extent permitted by applicable law, Self-Serve subscription plans automatically renew at the end of each subscription period unless canceled at least one day before the renewal date listed in your Billing Settings."
https://help.vimeo.com/hc/en-us/articles/12425398980625-Vime...
(I did look through their terms, and it doesn't disclose the precise time they will bill, they only referred to dates)