Is it normal for ginger paste to spit violently in oil?
This is more likely due to the other ingredients in the paste (sugar, citric acid, vinegar and salt; mainly the vinegar) hitting the hot oil. It's the same reason you never throw water on a frier fire. Oil and water/vinegar don't mix!

You can avoid it by not being lazy and using fresh ginger, which is much nicer anyway, or adding the ginger to the oil before it gets too hot.