I don't understand very well how the implementation is but there are several ways, Tilemap has several functions, including creating an ingame tile, example:
$ TileMap.set_cellv (tilemap.world_to_map (get_global_mouse_position ()), 0)
In this example I use the mouse position to create tiles while I move it, look at the
world_to_map (Vector2) function, what it does is pass the world coordinates (Increase by one for each pixel) to the tilemap coordinates (increase by one by each tile). The integer at the end indicates the tile id, which are unique for each tile in the tilemap. Using -1 removes the tile in position. If there is another tile already drawn it is replaced.
What I would do is include a Position2D node as the child of your animated sprite (or use the sprite position), at the tip where it draws. Then I would use its position (Your global position) in the set_cellv () function to draw the tiles as it moves. Example pseudocode:
$TileMap.set_cellv ( $TileMap.world_to_map($Sprite/Tip.global_position), 0)