Based on your update I think this is the simplest way to achieve what I believe you want:
express = 1;
tSet = Range[1, 5];
Table[express, {t, tSet}]
{1, 1, 1, 1, 1}
express = t^2;
Table[express, {t, tSet}]
{1, 4, 9, 16, 25}
You lose the direct vector evaluation of Listable functions but this is both more general and a solution to your specific request.