So, it turns out that the cheap Digispark clones do have a slight difference from the real thing - pin p5 is a "reset" pin by default.
Imagine my surprise, when the project I was working on starting doing some seriously strange things when I connected a push button to that pin 
The procedure to make that pin into an I/O pin is not too bad, but involves a bit of extra wiring and command-line cryptic sort of updating.
I had to solder on temporary headers to make the connections, and use an Arduino UNO as ISP.
(The remote control is to avoid shorting out connections.)
It's definitely a lot more work to fix issues like this AFTER the project has been assembled
The good news is that all of that mess of wiring you see in the background actually (surprisingly!) worked perfectly the first time.... after I changed that reset pin issue, and re-connected all the wires I had disconnected as part of debugging the issue. sigh.
Best,
-Nico