We have a Vios, 2010 E/AT

I've experienced what you just posted. But it occurs rarely (like once in a year).

After the engine has started, it misfires, then idles up.

Lately, I did the liberty of pulling out the spark plugs and re-gapped them. Hindi na nangyayari so far.

It seems like the casa mechanics beforehand just installed the plugs without checking the gaps. Puro out of spec lahat.