Any Experts here who can help solve this please.. Thank you for your support.
An action filter is going to filter out actual rows. As best as I can tell, you're not going to get this to do what you want it to do. Essentially you want the bar chart to give you the same running sum that you have in the line chart. With rows filtered out, that's not going to happen.
Can you change your design to click on a parameter value, or have the user enter a parameter value one way or another? If so you can have the bar chart filtered using a table calc to display just the running sum value for the selected month.
You may want to have a look at this: Re: Running Average
where I did something similar for running average. Here it is in tableau public:Tableau Public
Note the solution uses nested LoD calcs which hits performance heavily so it might only be feasible with relatively few running partitions (e.g. months).
I've been playing around with your workbook but I don't think I can come up with a solution that fits your need exactly. The previous suggestions are the only other things I can think of, probably the parameter option specifically.