You will need the tool, a new plunger tube and you must make sure the mounting holes inside the frame are countersunk. If you try to restake one that has worked loose it will just keep coming off. The reason it came off is almost always because the holes weren't countersunk for the mounting post's tips to expand into or the posts were not long enough. It works just like a rivet.
from what i can tell is that they were never staked at all in too the frame, i looks like they were just red locktite in their. the piece dont seem to have any marks on them as if they were flaired at all.
Just out of curiosity, who manufactured your gun? This tendency to attach parts with adhesive only seems to be increasing in the last few years. I worked on Springfields and Colts for about 15 years and seeing a loose plunger tube was actually fairly rare. It seems to be happening on an awful lot of 1911s today. Locktite may hold it for a while but eventually it will fail. The plunger tube has to be mechanically riveted to the frame. The shop I worked for used to only charge 10 bucks to rivet on a new tube in the old days (and the cost of the part). A guy could make good money with these new guns. I have also heard that Springfield has been "gluing" their ejectors onto the frame for a few years now instead of pinning them.