[AndrewGSW]

If, as stated, this is a click and drag map them presumably the target-tile will be the same for both mouseup and mousedown.

You might consider my earlier suggestion:

var justClick = false;

someElement.onmousedown = function () {
    justClick = true;
}
someElement.onmousemove = function () {
    justClick = false;
}
someElement.onmouseup = function () {
    if (justClick) {
        // show menu..
        return;
    }
}

Although it's hard to be certain without further information.