SSIS Output File column headings in first row property not working

I am using Visual Studio 2017 and have an SSIS solution that is outputting to a flat file.
My first process loads the data from one file and puts the headers in the first row as it should. I created another connection manager for the second file that points to the same file with an append and I set the column names in the first data row property to false. However, when I run it I get a second set of headings in the middle of the file. Any help would be appreciated. I am fairly new to SSIS and I'm kind of learning on the fly.

Thanks!

For the second connection, what is the setting for the heading row?

It’s set to false – that’s what I don’t understand. Seems like it should not output the headers if that property is set to false.

Hard to know what's going on without seeing the whole package. but that's too big to post, I guess.

Instead of appending to the existing file - wouldn't it be easier and better to use a union to join the data from each source and then output to a single destination?