I've tested how the filter icon's position is affected when a header template is set and didn't notice any difference.
For example, with the following template: "<span style='background-color: lightblue; color: black;'>Some text <strong>bold text</strong></span>"
the Grid looks like this: https://www.screencast.com/t/YQrfdtp3
So, could you post your template so we can check whether there is something specific about it that causes the icon to be displayed on the left side?
The template posted above shows how to style its content's color and background color. Alternatively, you can set a class to the elements within the template and use the class in CSS rules, to achieve the desired appearance of the Html within the header template.
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