Go read my other responses.
You think the amount of ash coming down will be like a little snow flurry—like mt St. Helens. Your understanding is wrong by about a degree of one thousand.
Again, I am not saying this will happen. This is purely a thought exercise. But you have to understand that such a tectonic event will change everything. Not kidding. If you do not have pure water in your safe place, you will run out quickly.
The water becomes horribly acidic. Just because of the minerals it will be seeping through. Think sulphur, iron, and all sorts of crappy minerals that make drinking water bad.
If you are relatively near that thing, you will either move south, or you will die.