It inserts only into the first table, because you end te trigger before the second insert.
create trigger tr_em
on emp
for insert
as
begin
declare @empname varchar(20)
declare @lastname varchar(30)
declare @address varchar(20)
declare @DOB datetime
declare @salary int
select @empname=empname,@lastname=lastname,@address=address,@DOB=DOB,@salary=salary from inserted
insert into emp_insert values(@empname,@lastname,@address,@DOB,@salary)
end
insert into emp values ('esdfs','sgssadsdgs','sgsadags','2jan 1878',5456555)
end
select * from emp_insert