You almost had it covered, but you mispositioned the added code. Here is the finished product for you:

menu status,menubar,channel,query {
  Nick Alert
  .set $iif(%alert == on, OFF, ON ) :{
    set %alert $iif(%alert == on,off,on)
    echo 3 -a nickalert is now turned %alert
  }
  -
  .set alt. trigger {
    set %altnick $addtok(%altnick,$$?"enter an alernative nickname here:",124)
    echo 3 -a your alternative nick $! has been added to my alternative list!
  }
  -
  .del alt. trigger {
    if ($istok(%altnick,$$?"Enter an alernative nickname to delete:",124)) {
      set %altnick $remtok(%altnick,$!,1,124)
      echo 3 -a your alternative nick $! has been deleted successfully!
    }
    else {
      $input(The alternative nickname $! is either deleted or doesn't exist in my alterntive nick list.,o)
    }
  }
  -
  .set nick to ignore {
    if (!$istok(%ignick,$$?"enter a nickname to ignore:",124)) {
      set %ignick $addtok(%ignick,$!,124)
      echo 3 -a $! will now be ignored!
      return
    }
    echo 3 -a $! has already been ignored.
  }
  -
  .del ignored nick {
    if ($istok(%ignick,$$?"enter a nickname to remove from ignore:",124)) {
      set %ignick $remtok(%ignick,$!,1,124)
      echo 3 -a $! is now removed from my ignore list!
      return
    }
    echo 3 -a $! is not found in the ignore list.
  }
}
on $*:text:$(/\b(\Q $+ $me $+ \E|\Q $+ %altnick $+ \E)\b/iS):#:{
  if (!$istok(%ignick,$nick,32)) && (%alert == on) && ($active != $chan)  {
    echo -a 4[ $+ $time $+ ] $nick said your name in $chan $+ : $1-
    beep 3
  }
}

I've taken the liberty of adding a couple of checks, along with an if statement to ignore added nicknames.