What is likely to have happened with these newly discovered antarctic volcanos below the ice?
That's a very interesting study, but only provide very rough information on the posible volcanoes that might exist under the ice.
In the case of the volcanoes shown in the radargram I'll highlight some points that might be the source of your confusion:


The tephra layer that overlay the volcanoes in the radargram was not erupted  by those volcanoes. It was most likely erupted by a volcano from above the ice (subaerial), or a subglacial one far away. It was later buried deep in the ice by the snow falling on top. Otherwise the layers would be much messier in the area and of varying thickness.
If those cone are volcanoes, its shape suggest that they were formed before they became covered in ice. Subglacial eruptions form flat-topped volcanoes with steep sides calles Tuyas, and what is observed are broad shield-type cones, that suggest submarine or subaerial formation.
They don't know if those volcanoes are active, but if one were to start an eruption, wouldn't be of the explosive type, because are likely to have fluid basaltic lavas, like the ones observed in Hawai'i. The explosiveness will come from the steam produced. It is hard to tell if it will blow the ice on top or not. It depends on ice thickness, eruption power, etc. But it is definitely a possibility for a strong enough eruption.