I think you need to let go of making a distinction where Japanese doesn't make one, just because English makes a distinction.
All ば in a first clause does is set up a hypothetical condition of a verb, and the second sentence then explains what would happen if that hypothetical condition was met.
In English, both ''If'' and ''when'' can do this. If is a standard condition. if x then y. ''When'' originally means a point in time. But if you're talking about a hypothetical point in time, then ''when'' can easily be used as a condition. Because ''when the point in time x happens, then y will happen. So when we want to emphasize time we definitely tend to say when. However in English we have an entirely different structure and different commonly used patterns that make things sound natural. That is very similar in knowing when to use all the other conditionals in Japanese. Only 1 of the conditionals truly means something different.
The particle と at the end of a clause indicates a state something is in. It is a logical condition. If x happens then y will happen, it's something to be expected. It's more used for facts. It can also be used just to indicate the state of something is in without even creating an if statement type thing. Like it does when you add と to an adverb, it just emphasises the verb was done in that state.
The rest of the conditionals are all different forms of the same thing that came to be used in different contexts and expressions. I'm not sure how the nuance differs.
As far as I know:
ば is a generic or hypothetical condition.
なら(ば). This is used for possibilities and consequences that someone would like to have. なら usually comes in response to what someone else said, . like ''If June goes too, I will join the party as well''. it's also used in certain fixed expressions.
There used to be a copula なり (copula=だ/です) and that's where ならば comes from, it's the hypothetical form of it.なら was the 未然形 form of なり, the one now mostly used to attach the negative ない to a verb.
たら(ば)is a conditional that comes from the helper word たり that would attach to a verb, たら is the shortened hypothetical version of it. It has more emphasis on the condition itself rather than what happens after. Maybe that's because it resembles the past form of a verb, I don't know, but that seems to be the nuance it has.