Having a tsunami early warning system isn't really the problem, they just did not think it was required to install it at this location as something like this has not happened before in recent history. If it had been in place it would have alerted since most such systems simply work with buoys in the ocean that detect a sudden increase in sea level.
Anak Krakatoa is fairly active at all times, but this came as a surprise result. It wasn't a full on explosive eruption but more of a ground move/slide effect (still unclear about the details on that).
One thing to understand is that things like earthquakes and volcanoes belching up dust and ash are pretty common around indonesia, so as such often little cause for concern. I've experienced a few just as a visitor, i reckon if you live there permanently you'd think little off it if the ground shakes around a bit.
Something like the 1883 eruption would still be a very fatal event, but there are quakes in the country that cause moderate to severe damage that do not get reported on internationally much. A few months ago we had the quake near Lombok island causing a lot of damage. No tsunami to speak of, but it did damage a lot of buildings and took numerous casualties as well.