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It's safe if you increment by the number of encrypted blocks. It's not safe if you always increment by one (which is what the tutorials said), as you would end up with the overlap you describe in your answer.
Fair enough, I didn't notice the ctr value vs. IV thing. I was not aware that the split counter was not standard, especially since several tutorials actually recommended using a counter as IV for AES-CTR to avoid IV reuse, which would be extremely unsafe without split counters...
