Though it isn't specifically about transits, Jakob, this article might be of interest to you:
The Classical Origin & Traditional Use of Aspects. Specifically, the section titled
'Application' & the Development of Orbs.
an excerpt:
Orbs originated from a need to determine a limit at which the strength of an aspect calculated by degree overcame the relevance of an aspect calculated according to the signs. It was essentially an attempt to define 'perfection' - the period of the aspect's strongest force. Usually this was interpreted as the degree of exactness, but opinion varied and the 2nd century text of Antiochus mentions 'contact' or "application in the proper sense" as occurring within 3 degrees.
I think the last sentence there holds the answer you are looking for: "opinion varied" but it was understood that the closer the orb the stronger the effect.
I've had events occur in my life before an aspect became exact. For instance, my father, who can be signified in my chart by the Sun because the Sun rules my 4th house (father), passed away when transiting Jupiter (the ruler of the 8th in my radix) applied a square to my Sun - it was still a degree from exact when he passed.
I think it's important to remember though that while transits, no doubt, can show events, there's usually more than just the one transit taking place, and other timing techniques should be considered as well. For example, the personal illustration I gave above, the death of my father as transiting Jupiter applied a square to my radix Sun, occurred weeks before I turned 35. Jupiter was transiting the same sign it was in when I was born (making a 'return'), completing its third cycle of rounding my whole chart. So I'd already had this same transit twice in my life. Why did what happened happen this time? I could go into further detail and tell you what else was going on in my chart at the time: transits, profections, directions, and so on that co-sign the specific event that occurred, but I'll spare you from having to sip on that muddy water - it's not the point of what I'm getting at. My suggestion to you is, take a look back at your chart and see what else was going on when the events you told us about happened. I'm sure you'll find some impressive things.