If it was security, I'd expect that it wouldn't update the original table and a rollback would occur. Is that what is happening?

Also, I'd write it in case multiple rows are updated. If it never happens, you haven't lost anything. If it does, then you've written bad code, and it doesn't take any longer to write:

UPDATE test1.dbo.tblUser

Set ext = @ext,

ext2 = @ext

where loginname = @user

than it does to write:

UPDATE a

Set ext = t1.ext,

ext2 = t1.ext

from inserted i

inner join test1.dbo.tblUser a

on a.loginname = i.loginname