Hi, 

A consulting arborist may be able to better tell you the appropriate window. Feel free to ask for a second opinion. 

Colorado State University states that it has a more flexible window for applications but up until early July. In the chart on the linked page it says mid spring is the optimum range. 

Spring would be the most beneficial time period because the sap needs to be flowing in the tree to have the chemical move through the entire system. You can also refer to this publication on optimum timing. I tried to highlight the relevant part but it is on page 6 if it doesn't show you. 

We think that the spring up into June would be better but if the tree company is wanting to start applications due to the severity of the infestation and the tree health it seems like September is the next best time. The label for emamectin benzoate (Treeage) states that it should not be applied above temperatures of 90 degrees as it could harm the tree further. 

Let us know if you additional questions. 

Emily