Block with content -> script after loading via storageManager

I have a component and a block defined inside my plugin. The block relies on fetching some data via AJAX and then re-rendering itself.

content: {
        type: "testComponent",
        content: 'AJAX loading...',
        script: function() {
           // content is changed via $("#" + this.id)
        }
    }

When I d&d block to the editor canvas all works nice. But once I load the stored data, script is not executed. It can be seen in the image that component type is saved and loaded correctly, hence the traits are there:

This is the same block, freshly dragged to the canvas -> it shows "AJAX loading..." at first and then JS in script is executed:

How could I execute the script of loaded components?