How to understand the mathematical constraint of potentials?
I suspect there's some misunderstanding about the definition/meaning of $a_{ij}$.  The time to complete task $i$ depends only on $i$ (not on $j$), so it wouldn't make sense to use notation like $a_{ij}$ for the length of task $i$: we'd instead expect to see only the index $i$, but not $j$, appear in that notation.

I suspect you'll probably need to go back to your textbook or other source on scheduling and look for a precise definition of the notation that it uses.  If your textbook doesn't define its notation, look for a better textbook.



As far as the constraint $t_j - t_i \le a_{ij}$, that is expressing that $t_j$ should start at most $a_{ij}$ seconds after $t_i$ starts.  So, it'd make more sense for $a_{ij}$ to be a permissible delay that expresses the maximum time you can wait to start task $j$, once task $i$ has been started.