See image below:
To get this I typed
@property<TAB><TAB>string<TAB><TAB>
It seems to depend a bit on the speed at which you type but do it fast enough and you get the popup menu.
I like to keep stuff aligned so I use TAB (which is set to 3 spaces here fyi) a lot and I have to backspace the @abstract out every time.
And regarding property-read & -write: I've seem to missed that it does pick up the property-read. However property-write seems to be unknown:
I verified my phpdoctags.cfg and it was missing from it. I added both read and write manually a while ago but it seems the -write disappeared (probably during an update).
Re-added it, but properties defined with it do not turn up in the code navigator (probably has nothing to do with the config file either).