first of all, sorry if I didn't notice it before, but I see that you're reusing the same map for each update.
This is not supported, please check the ItemEventListener class description.

At a first look the rest of the code seems ok, maybe you used the wrong name client side.

You can send any string through Lightstreamer, but, as long as you plot your chart with our ChartTable, any value on the axis must be a number. You can easily convert your date client-side as we do on the ChartDemo. Don't know about adobe chart libraries.