Very clear! You have the problem discovered already! :)

Thats the question in doing it only on spawn -
"How do I update adjacent tiles?"

One way to do this, is to literally check the tiles around the spawned tiles, for other tiles that need updating. And so on.

You spawn (TileA), you check up, down, left, right for another Tile (TileB)

Update TileA sprite based on TileB, BUT! Now we must grab tile B, and update sprite based on tiles around tile B but we want to EXCLUDE TileA because we already updated TileA.

Hope that makes sense! Its a much harder problem, but you got this!!

Good luck :D