Dear $p^4$,
I had a chance to glance further at the 4 author paper linked in your comment. Their connection form is $-dt + sdt/t$. This has double pole at $\infty$, so it isn't regularregular*. However, the connection in your question has logarithmic singularities at $0$ and $\infty$, so it is regular, as I said earlier. There is no contradiction.
*(Afterthought) This is a bit sloppy, since the Fuchs criterion is only a sufficient condition for regularity. But to see the non regularity, observe that the solution they write down $exp(t)t^{-s}$, which is correct (!), has bad singularities at $\infty$.
