Looking at the code, there are 3 places the EasyPost Rates API is called:
Testing the settings in ACP.
Viewing a physical product's page (to figure out shipping rates/time)
The shipping step in the checkout process.
The code tries to retrieve the rates automatically only if you enabled the Allow Customer to Choose Rate? option in ACP.
When this setting is enabled viewing a physical product makes 1 request to the rates API. If a member refreshes the page 10 times or views 10 separate physical products, without purchasing anything, that makes it 10 API requests with no purchase.
This happens also when the page is being viewed by a bot. Maybe some bot aggressively indexed your site and caused all those requests? At the very least it should not execute the API call for bots, but I don't see any kind of block in the code right now.
I think there should be a warning added for this. Maybe this was not something EasyPost did when the API was initially implemented into Invision Community. 🤷♂️