For all positive powers of primes $p \geq 5$, we prove the existence of infinitely many linear congruences between the exponents of twisted Borcherds products arising from a suitable scalar-valued weight $1/2$ weakly holomorphic modular form or a suitable vector-valued harmonic Maassform. To this end, we work with the logarithmic derivatives of these twisted Borcherds products, and offer various numerical examples of non-trivial linear congruences between them modulo $p=11$. In the case of positive powers of primes $p = 2, 3$, we obtain similar results by multiplying the logarithmic derivative with a Hilbert class polynomial as well as a power of the modular discriminant function. Both results confirm a speculation by Ono. (joint work with Andreas Mono).