It seems extremely unlikely that both A/C and heat were running at the same time. If it happens again, check the outdoor unit to make sure that it is actually running. You might have a load control causing a delay in compressor startup, while the indoor blower fan starts running immediately.
My wyze thermostat is putting the heat and a.c. on when in heat mode exactly like this one.
A.c. works on its own if you just go to a.c. but both come on if you go to heat mode.
I disconnexted my outdoor unit by pulling the outside fuse until there are real solutions on here.
I had to follow a YouTube video to get the thermostat to work in the beginning by moving the Green wire to another terminal which cuts off the ability to turn the fan off and on.