Many internal martial arts practice pushing hands, but not all use the method of chi-intrusion. Chi-intrusion is defined as willingly connecting chi between two persons, usually between a master and a student. Some religious or spiritual practices make use of chi-intrusion, it is being called Crown Divination （灌頂). The simplest form of Crown Divination is pouring cold water over the practitioner's head, with the practitioner doing internal chi connection with his Divinity, and the chi of Divinity gets inside his body through chi generated by the cold pour. I personally saw this simple form done in some Thai Buddhist practice. The act of baptism in Christianity may possibility be a remnant of this practice. Serious Crown Divination usually involves the master touching a body part (or body parts) of the practitioner who is in a meditative, or chi-filled, state; and it does not necessarily mean touching the crown.
The use of tai-chi pushing hands for chi-building can also done with this chi-intrusion method (but not necessarily has to be done this way). And like the Crown Divination practice, it is clouded with myths and secrecy. I will try to discuss the issue here. Personally speaking, I don't like people's chi getting into my body. A part of the other guy's personality might get in too, depending on the aggressiveness of the sender. On the other hand, I will send out chi occasionally for healing purpose, when everything else fail, like an old man suffered from late Alzheimer's disease, and therefore lacks the volition to generate chi by himself. Because of my practice orientation, the discussion below will not be too experiential in nature, as you can expect that in other posts of mine.
In the first stage of doing chi-intrusion pushing hands, a practitioner will do guided free pushing hands with his master. He will be required to set his lowest chi strength (limiting case being zero) at the point of contact, usually hands and fingers. His highest point of chi strength will be his feet. A chi-gradient shall thus be formed. The practitioner is required to mindfully build or cultivate this chi channel, that will be changed and tested by the master. The criterion of success is that the student will be able to feel or listen to this chi-gradient during all the time he is doing guided pushing hands. This is called the stage of Chi-listening （聼勁）。
If the first stage is successfully accomplished, a student is ready for the second stage, it is called Chi-feeding (喂勁). In this stage, the master will try to add jing (or chi-power) to the student's point of contact step by step. Given the ability to maintain the gradient, anything added at the lower point will automatically (assuming successful) add to the whole chi-channel all the way to the feet. The criterion of success is that by a seemingly innocent touch, a student will fly out, and oftentimes jump a few steps up and down like a spring before standing firmly again. Interested readers can search the web and find out such demo videos. Of course, I shall expect people coming up with all different kinds of interpretations to these demos! My readers are free to buy any of these opinions, if they find mine too boring to be taken!
The chi-intrusion method is a very powerful method of building chi for a practitioner, assuming that there exists a matching pair of able master and able student, both having the aptitude and willingness to train and be trained. The fact is, as revealed to me by one such master, it is extremely difficult to find suitable students, and it would be lucky if a master can find a handful of students with the right aptitude to teach in a life time. So don't complain if your teacher uses this teaching method on some students and he didn't teach you this way - most likely there is something wrong with you rather than with him!