I would suggest that you run both the queries, one before append and one after append, separately and see whether both the "inversion" and "non inversion" queries return you the data in same timeline for which you are plotting. For example the way your graphs show up tell me that one of the query's data is for a time earlier than 15th Nov. In your case the blue graph which has data only for Nov 15th is trying to plot the data of 30 days ago as well.
In such cases you need to adjust the previous data's timeline to match to current data. So let's say if you wanted to compare one month's back data (not of entire month data but of a day 30 days ago) with today's data then you will have to shift the one month back data's timeline (yellow graph) to match it to current blue graph's timeline which is of today's timeline. I am adding the logic of how to shift this timeline in answer as well so you have both the graphs on same timeline.
Also since timechart will tend to bucket the numbers on its own based on the time range chosen so if you were looking for the total number of emails, yes it will be sum(count), whereas in cases where you want to deal with times, like response times charting, then maybe max, min or avg might be suitable. Updating the missing pipe as suggested in the answer.
See here for more insights on how to shift timeline to show on same chart.
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