I would like to point out that in the latest available version of Mobile Testing (220.127.116.11) the Refresh Agents button is removed and agents list refreshes automatically. Based on that I guess you are using an older version of the product.
Note that no matter what version you are using, the Mobile Testing supports web and native agents connected at the same time. I am attaching an image taken from the 18.104.22.168 UI while a Safari web browser and Mobile Testing iOS agent are connected to the runner.
Test your Android and iOS apps against any device or browser with Telerik Mobile Testing. Part of the Telerik Platform