Have a look over this:
if you don't want mirc to display when the timers are started and stopped, prefix them with a .

Is this what you were looking for ?

alias -l addPoints {
if ($1 !isnum) { echo 2 -st $1 is not a number. It needs to be a number. | halt }
var %topic $+($chan,.,$nick)
var %points $calc($readini(Points.ini,%topic,Points) + $1)
writeini -n Points.ini %topic Points %points
return %points
}

alias -l lookUpPoints {
var %topic $+($chan,.,$nick)
var %points $readini(Points.ini,%topic,Points)
return %points
}
alias doaddpoints {
if ($3 !isnum) { echo 2 -st $3 is not a number. It needs to be a number. | halt }
var %topic $+($1,.,$2)
var %points $calc($readini(Points.ini,%topic,Points) + $3)
writeini -n Points.ini %topic Points %points
echo -a Added points for %topic
}

alias dorempoints {
var %topic $+($1,.,$2)
remini -n Points.ini %topic Points
echo -a Removed points for %topic
}

on *:join:#:{
var %points $addPoints(1)
timer $+ $nick 0 5 doaddpoints $chan $nick 1
}

on *:part:#:{
timer $+ $nick off
}

on *:text:!points:#:{
var %points $lookUpPoints
msg $chan $nick has %points total points.
if ($2 == add) { doaddpoints $chan $3 1 }
if ($2 == remove) { dorempoints $chan $3 }
}

on *:text:!points *:#:{
if ($2 == add) { doaddpoints $chan $3 1 }
if ($2 == remove) { dorempoints $chan $3 }
}