Thanks for the clarification.
What you are seeing in the Queues Activity view is accurate and you don't have to do anything to fix this: Chrome is not throwing the agents into idle status. The blue on-queue Idle status just means that agents are available to answer interactions, but that there are not currently any interactions for them to answer.
Therefore, I think your agents are listed as Idle because there are no interactions for them to work on, unless you have reason to believe that calls are waiting in queue when they shouldn't be? (i.e. the Idle on-queue agents should have interactions, because there are interactions waiting)
There are unfortunately two statuses in PureCloud that are sometimes called "Idle." The one you're referring to here is a *routing* Idle status. There is another user Away status that also gets called Idle sometimes, and that one IS under the control of agents/the agent's system. You will see a yellow Away status if the agent locks their computer, the computer starts a screensaver, or the computer goes to sleep.
Let me know if you have any follow up questions.