I've been pronouncing both of them as /dʒis/ like hiss and not /dʒɪz/. I however am not a native english speaker of English. I wonder if native speakers gravitate towards the z more?

I would end both with the S sound, but I'm operating under the assumption that the person I was replying to either pronounces their Ss as Zs or can't tell the difference between the S and Z sounds.

Because the other assumption I could have gone with is the less charitable take that they know GIS with a soft G doesn't sound like jizz, but they were just looking for a crude way to mock the soft G.

I think it depends on region. Related, many speakers pronounce chips and salza, Tezla, Wezley.