> I expected vimiv to start as a background job in the current terminal and then receive a sighup when the terminal is closed and also exits.

No, that's not what happens. `vimiv` would only get a `SIGHUP` signal (from the kernel) if it was a *foreground* job, or if it was a *stopped* background job. But it's neither: it's a running background job.

Or if bash (bash in particular, not any shell in general) had itself received a `SIGHUP` signal and has resent it to all its non-disowned jobs. But in your example the shells exits normally via `exit`, not because it was signaled by `SIGHUP` [1].

> For example, if I execute `vimiv &` followed by another `exit` command, `vimiv` will close

That may be something special to that `vimiv &` program -- if I enter `xclock &` and then `exit` on a separate line in a terminal, `xclock` will not terminate. It will however terminate if I close the terminal from the `X` button, because in that case `bash` will receive a `SIGHUP` signal and will resend it to `xclock`.

[1] bash can also send a `SIGHUP` when exiting normally, but only with `shopt -s huponexit`, which is not the default.