It sounds like you just answered your question, that the Tapus aren't nature locked, but you're just getting unlucky with the natures you're getting.
I haven't tested it myself, but if Synchronize works on the Tapus, it might be worthwhile to get a Pokemon with Synchronize (and the same nature as what you want) to make it more likely you get the nature you need, especially if you're trying to get max IVs or lower IVs in a specific stat.