I can confirm this behaviour. To be honest I cannot give you an exact detailed description of what is happening, but it must be due to the fact that for the Popupmenu and the PanDragTool are using the same mouse button for activation. There is a mechanism in the ChartTools to allow using the same key for different actions. By calling PanDragtool.Handled in the right event it may be possible to pass the right-mouse-click on to the Popupmenu. However, I could not find a satifying combination; in the OnBeforeMouseUp event, for example, the popup menu did appear, but also when doing a normal drap operation...
But why so complicated? The menu and popupmenu commands in your example have the purpose to mutually interlock the zooming and dragging actions. Therefore, there is no need to assign different mouse keys to the operations. Set Shift of the PanDragTool to ssLeft (rather than ssRight), and the interference with the popup menu will be gone. Your program should work as expected.
Moveover, your sample project is a nice demonstration how code can be simplified by using Actions. Therefore, I am attaching a modified version of the code in which two TActions, acZoom and acPan, do the work of activating/deactivating the chart tools. And after assigning them to the items of the MainMenu and the PopupMenu, as well as to toolbar buttons, you get handling of these tasks for free.