Normal orientation works:
[FEN ""]
[StartPly "2"]
1. e4 {[%draw arrow,e2,e4,red][%draw full,e1,green]}
Flipping sides doesn't move the drawings:
[FEN ""]
[Startflipped "1"]
[StartPly "2"]
1. e4 {[%draw arrow,e2,e4,red][%draw full,e1,green]}
Tested in Microsoft Edge 104.0.1293.54 and Firefox 103.0.2.