The very highest output voltage you can expect from this circuit with the chip in regulation is about 3.7V, so a 1K pot would be more appropriate. In fact you should allow a bit of margin, so maybe 3.5V maximum.
Using a pot as a rheostat is bad, using it as all the resistance is worse, and using only 20% (or less) of the element is really, really horrible, even if it's a good pot.
A 1% of full scale change in that pot means the output voltage will change by 5%, or 165mV if it's 3.3V.
If you're interested in millivolts, you should definitely limit the range of adjustment as much as possible. For example, if you need 3.3V you might use a 100 ohm pot with 787 ohms in series and an 499 ohm resistor for the bottom part of the divider.
For even better performance, shut the pot with a precision resistor of perhaps 1/10 the value and use it as a voltage divider. For example, a 1K pot used with a 110 ohm shunt. Then you could use a 452 ohm resistor for the and a 787 ohm resistor as follows:
simulate this circuit – Schematic created using CircuitLab
A 1% of full scale change in the pot position will change the output by about 0.2%, which is 100x better than your circuit, whilst still using very inexpensive components. The purpose of shunting the pot is two-fold- pot elements have lousy tolerance compared to resistors and this reduces the variation, and they have lousy temperature coefficient so that is proportionally reduced. Using it as a voltage divider virtually eliminates errors due to contact resistance variation (CRV).
You're also putting considerable current through the TLV431, presumably so you can draw a lot of current from it. Consider using a lower current and buffering the reference- it will reduce temperature-related drift of the bandgap reference. Trade that off against the inaccuracy caused by a high impedance in the feedback terminal.
(of course the above example value are just for illustration- substitute your own requirements and do the math for your situation).
Maybe replace Q4 and the reference diode with a super-cheap (pennies in quantity) TO-92 TL431 and two 1% resistors set up to maintain the -6.9V voltage where the emitter of Q4 is connected. The 560R resistor can stay if it is 1/4 W or better, just remove Q4
Resistors would be something like 4.99K and 2.80K.
In other words, connect a shunt regulator between 0V and -6.9V nodes, and use the existing 560R resistor to pass 16mA through the shunt regulator. It will typically drift about 50ppm/°C. (the 560R resistor will be on the other side compared to the below schematic)
Of course there are much better shunt regulators available but I'm not sure the difference would be worth it.
Best Answer
The 5ppm is only a typical spec, and there is no guaranteed maximum. Also the 35ppm is a typical spec (of total resistance drift). Note that the 3-sigma element resistance drift over lifetime is in the hundreds of ppm so some parts can be pretty bad. You don't see those changes directly in your configuration but they can result in side effects if there are temperature gradients on the chip (from internal or external heat flow) or stresses.
The tempco of the 'wiper' resistance is surely much, much higher but you say you will buffer that so it may not be an issue. It will also be somewhat sensitive to supply voltage.
When you get down to the ppm level things like the stress on the die (from board flexing, from soldering, from environmental changes) can affect the value of "semi-precision" resistors like the on-chip parts in question. If it's designed to be a high precision part they can put extra cost in there to compensate (perhaps by using symmetrical resistors that compensate for each other). We don't really know how carefully they've designed that chip.
I don't see what good a SPICE model would do you for a part like this- you're looking at deviations from the nominal so a calculator and sharp pencil (and a caffeine-sharpened mind) are usually your best tools.
Bottom line- if you need guaranteed specifications you should specify parts with guaranteed performance. Otherwise you may find yourself trying to make a silk purse of a sow's ear.