Technically a sticky stat could cause the water to boil and force it out, but its far more likel to be the rad cap to be honest, especially if youre not seeing overheating too. A new rad cap from Toyota is only a few squids and is your best first port of call IMO. Yup, I asked about the manual because I think the official bleed technique is in there but Ive not read it for a while and just gave you the way that works fine for me.
As said above, if the cap has a dodgy seal/spring it releases water too easily and the system never really gets up to pressure, meaning the water finds it easier to boil and expands into the expansion tank more easily.
Just make sure you're not over-filling the expansion tank, it's designed to allow expansion and contraction so it should not be full, it has max and min marks on it but they're often near impossible to see, I just bleed mine and ensure a couple of inches of the tip of the expansion tank down-hose (the hose that comes down from the tank lid) dips into the water.