When using "alias has its own outgoing server" -- not necessary to configure alias in web mail, whatever the mail service.
When NOT using "alias has its own outgoing server" which is the default -- i.e. the app would send messages "From: alias" through the parent account's outgoing server:
Then it's always necessary to configure the alias in the mail service (web mail), so the outgoing mail server allows login as "the account" and "From: alias" (a different address).
Now Hotmail:
Before the recent / ongoing / still finishing Hotmail server upgrade --
-- Hotmail's SMTP would *always* rewrite the "From: alias" and make it "From: primary identity", where "primary identity" was a Hotmail thing, initially the account's address, but could be something else, in web mail settings.
Now, since the server upgrade --
-- Hotmail's SMTP does *not* rewrite the "From alias" and so it's possible to send messages from the alias, from AquaMail, through the account's (Hotmail) outgoing mail server.
The alias still needs to be configured in web mail, just like with other mail services.