Based on the documentation (http://www.iredmail.org/docs/sql.create.mail.alias.html), the alias table is used for mail alias acccounts. And the list members should have value 1 on column is_list.

One additional Question: what is the difference between is_list and is_alias and why should be, according to documentation is_list, be used for setting up aliases?

is_list is the mail alias account with possibly multiple recipients and access policy:
http://www.iredmail.org/docs/sql.create.mail.alias.html
So if you want to create an alias address that forwards email to multiple recipients, this is what you need.

is_alias is an alias per mailbox user:
http://www.iredmail.org/docs/user.alias.address.html
If you want to have multiple alias addresses for a mailbox, so incoming mail for all of them comes to same box, this is what you need.

One alias address in alias table can have multiple recipients in forwardings table (with is_list).

One mailbox can have multiple alias addresses in forwadings table (with is_alias).

One mailbox can have multiple forwarding addresses in forwardings table (with is_forwarding).

Also each mailbox has is_forwarding record for itself, to receive mail normally (both address and forwarding cols have same user mailbox address). To prevent receiving mail normally and only forward it, you can change active to 0 or delete the row.

Neither is_alias nor is_forwarding needs entries in alias table, so if you don't have any mail aliases (often called mailing lists) with is_list = 1 then alias table should be empty.