Lets do a quick back of the envelop calculation, shall we?
Scholz' star, actually a binary star, has a mass of 0.15 solar masses. It passes by from a distance of 0.8 light years which is about 160000 AU.
Jupiter's mass is about 0.001 solar masses, so 1/150th of the Scholz's star's mass. However, it is 'only' 5.2 AU from the Sun, so at the close approach, Earth is about 4.2 AU away.
We can now calculate quickly the ratio of gravitational effects that Jupiter and Scholz's star have on Earth during that close pass. Remember, gravity scales proportional to the mass, but inversely to the square of the distance. So:
Jupiter's effect / Scholz's star's effect
= (1/150) * (160000/4.2)^2 = about 10 million.
The difference of Jupiter's pull between the farthest point (~6.2 AU) and the closest (~4.2 AU) = (4.2/6.2)^2 = 0.46 => Jupiter's gravitational effect at the closest point doubles in comparison to its farthest away point. If you take into account that at the closest point, Jupiter pulls 'against' Sun, and at the most distant one, 'with' Sun, you could say that the net contribution changes three-folds. So about 30 million times the effect of the Scholz's star.
In other words, if Scholz's star's gravitational pull 70000 years ago from 0.8ly away would trigger a supervolcano on Earth, Jupiter would make that look like a fart in a bath every ~1.1 years when Earth does the closest pass (taking a bit longer than a year since Jupiter moves during the year, too).
And, as everyone knows, the Moon has even more of a gravitational effect on Earth than Jupiter (about 100 times stronger, due to being so close): the tides. I haven't been noticing supervolcanos popping out every 24h of the Earth's rotation, or even on a monthly cycle.