I read there was problems with the 380mA versions, which is why I bough 350mA from a UK seller off eBay. The listing had this image:

If it was the regulator that didn’t like the PWM, then there still would be some logic to the modes, which there isn’t. My thoughts are either a bad OTC or the hex file was for a ATTiny25. The OTC appears to be soldered correctly and I’ve traced the connections, which are fine. Is there a difference between the ATTiny13 and ATTiny13A? Do I need to recompile the code for a ATTiny13A?

I’ll try compiling the code later, flash another ATTiny13A and see what happens.