Hard-domed tweeters, in most cases, include what is called a "phase shield". This is usually in the form of a disc-shaped piece of material supported, in one way or another, directly in front of the dome and centered on it. It's not been used in hard-domed midrange drivers at all, to my knowledge.
There is at times some misunderstanding of just what this shield does. It doesn't alter phase per se, as it cannot alter the phase of the signal as it emerges from the dome. Its purpose is to block the output from the tip of the tweeter, the reason being that at the upper range of tweeters, somewhere around 10KHz and up, the signal emanating from the tip will actually arrive at the listener prior to that sound emanating from the rim, where the former attaches to the diaphragm. At high frequencies the time difference is significant enough that there is a phase delta that causes interference to occur.
The reason that this occurs is because a hard-domed diaphragm is pistonic to a much higher frequency than softer diaphragms. Essentially, the speed of sound is much faster in the hard material than it is in air, it therefore reachs the tip and emanates form it before the sound passing through the air originating from the diaphragm rim area can reach the equivalent distance out from the driver.