If you mean twitchy as in slippery, and in "normal" riding as you did for the first 50, then no, it's not normal, but I don't have an answer for you if the tyre is okay and pressure correct
On the other hand, I imagine it's perfectly possible to overheat a D220 rear if you're really "on it" hard for 20+ miles of the right kind of roads.
Touch it with your hand when it begins to happen, if it's genuinely overheated, it will feel too hot to keep your hand on for long.
I had D220s for a few thousand, replaced because of wear (second hand bike), and I noticed with the replacement "RoadAttacks" that they gave me a bit more confidence in the first few miles, especially if it's wet or damp. I reckon this higher general confidence level is the reason I am able to use the whole tyre, D220s had strips, but in retrospect I don't think this was due to lack of grip, just lack of confidence. The D220 is a perfectly usable tyre, switching to something else won't transform the bike (imo), which is what posts/threads might lead you to believe.
RAs aren't the best tyre either mind you, but they are cheap.