According to the same Javadoc:

If the argument is NaN or an infinity or positive zero or negative zero, then the result is the same as the argument. Can't do that with an int.

The largest double value is also larger than the largest int, so it would have to be a long.

Personally, I would write the code just as:

unsigned int x
unsigned int y

public void myFunction()
{
    getTile(x / 64, y / 64).doOperation();
}

since being a tilemap, you can use it (and thus assume) using positive-only values. This does not affect readability because x and y are declared as unsigned int, quite close to the block, and every programmer knows whether the language performs or not an integer division with the / operator when it is applied to two integers (most of them do). In fact, such a geometrical scenario is probably one of the few ones that shows that integer divisions can be useful.

Moreover, thinking about omptimization of such a snippet represents, in my opinion, one of those cases of "unnecessary preventive optimization": you can often assume that such operations will not be a bottleneck of your code, and thus take actions only when profiling shows the opposite. Performance of casting operations can be difficult to evaluate, in general: they largely depend not only on the language, but also on the compiler, which can remove unnecessary casts, or "translate" them in worse/better assembler.