The original "import culture" started more than 100 years ago. As in "the Bentley Boys". If you mean the "hot-rod culture", it dates to 1947 or so, when chop-top Fords were injected with large-block Chevy engines. If you mean "sport compacts" of sorts, then that would be about 1970, when the Datsun 510 and 240Z were all the rage (and the hot-rod scene had new muscle cars to play with). "Sport compacts" could also refer to the Alfa Romeo 2000GT & BMW 2002....
If you mean "import sport compacts in the US and from Japan" (which is what I think you mean), it started with the dirt-cheap Datsun 510. It faded until the early 1980's, when Honda started making headway with the Civic. If you followed the pattern above, the "fast car" culture followed whatever was brand or market cheapest at the time.
But there's a difference between the "fast car" culture and the "all show and no go" culture that is so permeable today. That crap started probably in 1994. Why? Because the Honda Civic was in such overwhelming supply, it was not only cheap to buy, but even cheaper to buy used. Pluswhich, it was actually good on the autocross circuit. The MTv ethos was nearing its peak, commercialising everything in its path. Having just irradiated moshing the year prior, street racing was getting full treatment. That was all go and little show, but in the MTv lemon-light, it was perverted into "wow, what hot-looking cars", emphasis on the looking.
Now we all know that teenagers will flock to anything remotely "underground" like ants to an anthill, but with all the direction of an earless bat. The result? NOPI.
And "Import Tuners" on Speed Channel. Can't beat hot, dumb chicks for good entertainment.