Lava eruptions like this tend to be less dangerous than ash eruptions, which can mess up air traffic and the ashfall is bad for the lungs and crops. So I don't think there's much cause for concern.
TIL volcanoes even have two different eruptions. I just always imagined they came with ash as a given. That makes me feel a bit better about this, though I still echo their hope for as little damage as possible.
I think it depends on the particular volcanoes. The volcanoes in Iceland and Hawaii, IIRC, have thinner and less gassy magma, so there's not as much gas buildup, and the eruptions tend to have more liquid lava. Elsewhere, say Mt. St. Helens, the eruptions tend to have thick lava, with lots of trapped gas inside, that tend to cause giant explosions, pyroclastic flows & big ash clouds.
I would hazard a guess that it's dependent on even more than region. Wasn't it an Icelandic volcano that shut down air travel because of ash a few years back?
When it erupts underneath a glacier, it causes huge clouds of ash to form. The volcano you're talking about (Eyjafjallajökull) is a glacier volcano in the highlands whereas this one is on the Reykjanes peninsula on the west side.
I'm by no means an expert but in Iceland,
eruption under a glacier = ash eruption
eruption not under a glacier = lava flow.
I'm sure it's more nuanced than that but it seems to be the rule of thumb over here.