Hello Bartek,
Thank you for explaining the issue in detail.
If you have set a limit from the product tag edit page, then you would need to set the limit for a particular user role from that product tag edit page as well.
For example, if you want to set a different limit for the Subscriber user role for a particular tag, then you would need to make sure that in the plugin settings, under the User Roles section, the Amount by user role option is enabled. Then go to Products > Tags > Your tag > Edit and there you will need to set the amount of Min sum [Subscriber] to the appropriate value.
Please give this a try. If you encounter any issues, then please let us know.
Kind regards,
Moshtafizur