I think it depends on how you're running Kibana. I'm running on CentOS 7 with Kibana installed from rpm packages and my logs have timestamps like this;
[vagrant@localhost ~]$ tail /var/log/kibana/kibana.stdout
{"type":"log","@timestamp":"2020-01-30T16:00:38Z","tags":["debug","plugins","usageCollection"],"pid":11419,"message":"Fetching data from kibana_stats collector"}
{"type":"log","@timestamp":"2020-01-30T16:00:38Z","tags":["debug","plugins","usageCollection"],"pid":11419,"message":"Fetching data from kibana_settings collector"}
{"type":"log","@timestamp":"2020-01-30T16:00:38Z","tags":["debug","plugins","usageCollection"],"pid":11419,"message":"not sending [kibana_settings] monitoring document because [undefined] is null or invalid."}
{"type":"log","@timestamp":"2020-01-30T16:00:38Z","tags":["debug","monitoring","kibana-monitoring"],"pid":11419,"message":"Uploading bulk stats payload to the local cluster"}
{"type":"log","@timestamp":"2020-01-30T16:00:38Z","tags":["debug","monitoring","kibana-monitoring"],"pid":11419,"message":"Uploaded bulk stats payload to the local cluster"}
{"type":"log","@timestamp":"2020-01-30T16:00:39Z","tags":["debug","monitoring","kibana-monitoring"],"pid":11419,"message":"Received Kibana Ops event data"}
{"type":"log","@timestamp":"2020-01-30T16:00:39Z","tags":["debug","monitoring","kibana-monitoring"],"pid":11419,"message":"Received Kibana Ops event data"}
{"type":"log","@timestamp":"2020-01-30T16:00:39Z","tags":["debug","monitoring","kibana-monitoring"],"pid":11419,"message":"Received Kibana Ops event data"}
{"type":"log","@timestamp":"2020-01-30T16:00:39Z","tags":["debug","monitoring","kibana-monitoring"],"pid":11419,"message":"Received Kibana Ops event data"}
{"type":"log","@timestamp":"2020-01-30T16:00:40Z","tags":["plugin","debug"],"pid":11419,"message":"Checking Elasticsearch version"}
How are you running Kibana?