past tense in adverbial phrases that does not mean past time

There are times when we use past tense to refer to future, like in the following sentences:

We'd manage the funds until he came of age.
You'd get helpers until you got older.

The background behind these two sentences was that a retail tycoon had a serious car accident and was in a coma. The first sentence was uttered when the tycoon's wife and partner were talking about who was going to inherit his shares if he had died. The wife answered their son, a teenager at that time, would.

My question is: why do we use past tense in came and got while in fact the tycoon's son was only a teenager at that time? Does it have to do with sequence of tenses?

By that I mean if we are talking about a counterfactual situation using the auxiliary "would", then the second verb has to be "came" and "got" respectively. Instead, if we replace would with will in those two sentences, then we will have to say

We will manage the funds until he comes of age.
You will get helpers until you get older.

Or do you have other explanation for the uses of came and got? Thanks a lot in advance.