This has been tested with build 4.2024.3.6 in the following way at runtime:

Open Chart with Point Series, populated with data:
- add average function and set datasource to first series
- Export chart to template stream, with data.
- Import template stream to new Chart

The second chart reflects the content of the first chart correctly.

test code:
========================
//  1) Save the template into a Stream...
System.IO.MemoryStream stream = new System.IO.MemoryStream();
try
{
	// save only Chart and Series formatting, NOT including data
	tChart1.Export.Template.Save(stream);
	// 2) Load the template into other Chart...
	stream.Position = 0;
	tChart2.Import.Template.Load(stream);
	// restore the chart alignment (in this example)
	this.tChart2.Dock = DockStyle.Fill;
	// repaint the Chart
	this.tChart2.Refresh();
}
finally
{
	// remove the stream, it's no longer necessary...
	stream.Close();
}

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Changes were made to a January build of TeeChart that resoved this issue.