How does ILM work?

Question

elasticsearch

Good day! I must say right away that I did not work with elastic earlier. Please help me for this.
What do we have. Raised on the docker ELastic KIbana Logstash. On the host deployed, for testing, Nginx and filebeat. Filebeat throws logs into Logstash, which is in elastic. In elastic everything comes displayed and visible. I configured ILM configured the index template, but the documents do not decrease, if you set a size limit, the size decreases, but there are no docks. I still can’t understand how often ILM works for each index, once at the time specified in the policy, or according to the global timer, say once every 10 minutes? Or am I doing something wrong? My configs are below, all done via kibana.

right before publishing, I caught the error
index.lifecycle.rollover_alias [nginx-2021-*] does not point to index [nginx-2021-000001]

ILM policy

PUT _ilm/policy/nginx
{
  "policy": {
    "phases": {
      "hot": {
        "min_age": "0ms",
        "actions": {
          "rollover": {
            "max_size": "300mb",
            "max_age": "30s"
          },
          "set_priority": {
            "priority": 100
          }
        }
      },
      "delete": {
        "min_age": "50s",
        "actions": {
          "delete": {
            "delete_searchable_snapshot": true
          }
        }
      }
    }
  }
}

Sample

PUT _index_template/nginx
{
  "template": {
    "settings": {
      "index": {
        "lifecycle": {
          "name": "nginx",
          "rollover_alias": "nginx-2021-*"
        },
        "number_of_shards": "1",
        "number_of_replicas": "0"
      }
    },
    "mappings": {
      "_routing": {
        "required": false
      },
      "numeric_detection": false,
      "dynamic_date_formats": [
        "strict_date_optional_time",
        "yyyy/MM/dd HH:mm:ss Z||yyyy/MM/dd Z"
      ],
      "_source": {
        "excludes": [],
        "includes": [],
        "enabled": true
      },
      "dynamic": true,
      "dynamic_templates": [],
      "date_detection": true
    },
    "aliases": {
      "nginx": {}
    }
  },
  "index_patterns": [
    "nginx-2021-*"
  ],
  "composed_of": []
}