OpenSearch - "Index permissions" for the role do not restrict access to the index

I have created the domain in VPC form with enabled Fine-Grained with internal database configuration (non-Cognito).
Now, I was tried to make an additional user with limited permissions to a single index by following this tutorial: https://docs.aws.amazon.com/opensearch-service/latest/developerguide/fgac-walkthrough-basic.html but in result:

• I can see only documents matched by "FlightDelay": true rule
• I can see anonymized Dest field
• I still can use the _search/ query, though I have limited it by the pattern opensearch_dashboards_sample_data_fl* for search only on the opensearch_dashboards_sample_data_flights index

Additionally, I have checked the same rules and settings on my local OpenSearch (also as 1.2) and there everything works as I expected. Did I forget about something or is there anything else that I must do?