How to make `st_join` stricter?

I used st_join() to combine t1 and t2.

library(sf)
j <- st_join(
  x = t1,
  y = t2
)

t1 represents voting precincts boundaries and t2, school zone boundaries. In some cases, the boundaries of t1 fit perfectly in one school zone but because the borders touch two other zones, st_join lines up a precinct with three zones.

How can I make st_join stricter so that if a precinct in t1 is mostly or seemingly entirely within a zone boundary of t2, the precinct lines up with only that zone, no others?