I completely believe that even if there are no aspects of transiting planets to natal planets we can still feel the transits. When they do aspect the natal chart planets, though, I think things get triggered, and not necessarily old material, although that certainly can happen.

Things are very funky for me with T Mars conj natal Uranus in Leo opp N Moon conj Chiron in Aquarius. OMG. I have taken to weeping, which is completely unlike me. Weeping over totally mushy stuff, and doing that PUBLICLY. YIKES! It is really uncool.

"I've read that some astrologers (on tribe, especially) don't consider the current aspects in the natural chart as affecting the natal chart of an individual unless actual aspects to that chart are made."

Hand basically says that we don't normally feel transits when they perfect because so many planets are transiting at the same time and interact with one another. The transits could hit you before or after aspect, depending on other factors. There are mid-point methods and such that he talks about in his Planetary Transits book that help you to figure out when to expect an important aspect to manifest.

The inner planets hit you faster and don't linger (usually), so their aspects aren't always as noteworthy as the outer planets (such as Saturn and Uranus), which are slow and build up. Maybe some of us are more sensitive to planetary transits than others, but I even feel Moon aspects every month, almost like clockwork, especially when it reaches my Sag Moon and squares my Saturn. They don't last long, but I notice them. Sad events and endings have happened for me on Sag Moon transits.