Previously users would use scripts using the official API to set the t-min to the date say weeks ago and run that script periodically.
See Year in review graph option - #2 by philip, which contains such a script, and How do I set the 'zoom' on my beeminder visualization to show 1-2 weeks max and not the entire time period?.
Then Beeminder added direct support for setting relative t-min dates on the webpage of a particular goal. As far as I know, there is no place on the website to set such as a default for new goals nor is there a way to set it across several goals all at once. Furthermore, having done that, the API can no longer be used to either get or set the t-min until the t-min is set on the website to a non-relative date, it seems.
There was a discussion in Discord about this at the time the feature was being implemented on the website. See Discord. A user suggested using ISO Date Durations to indicate the relative dates.