Well yeah, that's a given. The problem is getting the proper tile data into each tilemap object..I have no idea why it isn't working.
1) I can only get 1 tilemap object to load the proper tile data
2) The tilemap objects occasionally get the tile data mixed up (I assume this has something to do with loading the tilemap images externally)
I don't even know what else can be done - there aren't a lot of options.
I've uploaded a simple project folder here if you wouldn't mind taking a look. (Extract the Test folder onto your desktop for external files to work)