Monero Ring CT sj calculation
All of the arithmetic is done modulo $l$ here.  The notation is slightly confusing—I would have written it as: $$s_j \equiv \alpha - c_j\cdot x_j \pmod l.$$  It may not actually matter whether the integer representative you choose for the scalar is positive or negative; there are many equivalent choices of scalar that will yield the same result when you multiply a curve point by them.  (But the specific algorithm you use to compute scalar multiplication may impose constraints on the integer, like being positive and below a certain size.)