Is the random value created when the timeline is running, or is this more of a setting up a scene thing ?
If you unpack the random integer preset, it looks a bit like this
The random node can be free or time (it's set to time in the preset). Time gives a new random real in the range -1 > +1 every frame which is range mapped to the lo + hi settings. You need to add 1 because integer conversion rounds down (else you'd never get the highest value).
Time gives a predetermined sequence based on the seed, Free gives a different sequence, new value every frame and also if you click in the viewport (or keep resetting F to 0).
So - more info needed.