An automation rule is configured for the Project where:

1. Issue is transitioned from Status1 to Status2
2. A transition screen pops up with a "User picker Field"
3. Field is assigned with a value
4. Automation rule that is supposed to pick the value of the above field and put is as Issue Assignee.

When automation run and issue is assigned, the results are not replicated on the screen immediately, until the issue is manually refreshed.

Note 1: This is sometimes intermittent and the Field Assignee does actually get updated sometimes immediately.

Note 2: This is not restricted to Assignee or user picker field, this happens with any field/custom field.

The above is because all Automation rules in cloud always run asynchronously, which means you can never guarantee the page to be refreshed.

It would be nice to to have these automation Rules run within the process (like they do in Server) so that the changes get reflected immediately.

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For a customer having both automation enabled, it is observed in Team managed project that Automation and Legacy Automation are always present in the left sidebar when they open the page from Project Settings. But when they refresh the page then Automation appears in the sidebar after a lag of 1-2 seconds.