When I "do" the pool chemistry I wear old big Elton-John 80s glasses, just in case there's any acid splash. And big rubber gloves.
When I was an early teen I played with chemistry sets and had acids way stronger than the ones you put into the pool. As I remember, and my memory might be wrong, some of the stronger concentrations didn't burn right away. There was, in effect, a delay. Then you were in trouble!
Today I carefully measured the readings and as always, needed to put a quart of acid into the pool. I thought I was being careful, but two drops splashed from the pool to my face and neck. IMMEDIATELY you know! It's a quick trot to douse it with water.
I don't know what you do if you fall in with the jug, because you'd hit the area with the acid in it AND the jug might explode - you never add water to acid, it's the rule: add acid to water. So whatever got into the bottle would cause a very violent reaction.
I've rinsed where the drops hit but I can still feel them burning.