Here's a debugging SSCCE  (Short, Self-Contained, Correct Example) based on your code.  There are assertions in this code that fire; it runs, but is known not to be correct.  I've renamed bottom to btm and oldBottom to oldBtm so that the names are symmetric; it makes the code layout more systematic (but is otherwise immaterial).
#include <assert.h>
#include <stdio.h>
typedef struct Point { int x, y; } Point;
typedef struct Rect  { struct Point xx, yy; } Rect;
enum { size = 2 };
typedef enum { colourGreen = 0, colourBlack = 1 } Colour;
/*ARGSUSED*/
static void drawRect(Rect r, Colour c)
{
    printf(" (%3d)(%3d)", r.xx.x, r.yy.x);
}
int main(void)
{
    Rect top[size], oldTop[size];
    Rect btm[size], oldBtm[size];
    int counter = 0;
    for (int i = 0; i < size; i++)
    {
        top[i].xx.x = 240 -  4 * i;
        top[i].xx.y =   0 + 10 + i;
        top[i].yy.x = 240 - 14 * i;
        top[i].yy.y =   0 + 20 + i;
        btm[i].xx.x =   0 + 72 * i;
        btm[i].xx.y =   0 + 10 * i;
        btm[i].yy.x =   0 + 12 * i;
        btm[i].yy.y =   0 + 20 * i;
        oldTop[i] = top[i];
        oldBtm[i] = btm[i];
    }
    while (1)
    {
        if (counter++ > 480)  // Limit amount of output!
            break;
        for (int i = 0; i < size; i++)
        {
            //in Struct Rect, xx is the top-left corner point, and yy is the bottom right
            top[i].xx.x--;
            top[i].yy.x--;
            btm[i].xx.x--;
            btm[i].yy.x--;
            if (top[i].xx.x < 0)
            {
                top[i].xx.x += 240;
                top[i].yy.x += 240;
            }
            if (btm[i].xx.x < 0)
            {
                btm[i].xx.x += 240;
                btm[i].yy.x += 240;
            }
        }
        for (int i = 0; i < size; i++)
        {
            assert(top[i].xx.x >= 0 && top[i].yy.x >= 0);
            assert(btm[i].xx.x >= 0 && btm[i].yy.x >= 0);
        }
        for (int i = 0; i < size; i++)
        {
            drawRect(oldTop[i], colourBlack);
            drawRect(oldBtm[i], colourBlack);
        }
        /*call delay function that wait for Vertical Blank*/
        for(int i = 0; i < size; i++)
        {
            drawRect(top[i], colourGreen);
            drawRect(btm[i], colourGreen);
            oldTop[i] = top[i];
            oldBtm[i] = btm[i];
        }
        putchar('\n');
    }
    return(0);
}
As noted in a late comment, one big difference between this and your code is that oldBottom in your code is declared as:
Rect top[size], oldTop[size];
Rect bottom[size], oldBottom[i];
using the size i instead of size.  This probably accounts for array overwriting issues you see.
There's a second problem though; the assertions in the loop in the middle fire:
 (240)(240) (  0)(  0) (236)(226) ( 72)( 12) (239)(239) (239)(239) (235)(225) ( 71)( 11)
 (239)(239) (239)(239) (235)(225) ( 71)( 11) (238)(238) (238)(238) (234)(224) ( 70)( 10)
 (238)(238) (238)(238) (234)(224) ( 70)( 10) (237)(237) (237)(237) (233)(223) ( 69)(  9)
 (237)(237) (237)(237) (233)(223) ( 69)(  9) (236)(236) (236)(236) (232)(222) ( 68)(  8)
 (236)(236) (236)(236) (232)(222) ( 68)(  8) (235)(235) (235)(235) (231)(221) ( 67)(  7)
 (235)(235) (235)(235) (231)(221) ( 67)(  7) (234)(234) (234)(234) (230)(220) ( 66)(  6)
 (234)(234) (234)(234) (230)(220) ( 66)(  6) (233)(233) (233)(233) (229)(219) ( 65)(  5)
 (233)(233) (233)(233) (229)(219) ( 65)(  5) (232)(232) (232)(232) (228)(218) ( 64)(  4)
 (232)(232) (232)(232) (228)(218) ( 64)(  4) (231)(231) (231)(231) (227)(217) ( 63)(  3)
 (231)(231) (231)(231) (227)(217) ( 63)(  3) (230)(230) (230)(230) (226)(216) ( 62)(  2)
 (230)(230) (230)(230) (226)(216) ( 62)(  2) (229)(229) (229)(229) (225)(215) ( 61)(  1)
 (229)(229) (229)(229) (225)(215) ( 61)(  1) (228)(228) (228)(228) (224)(214) ( 60)(  0)
Assertion failed: (btm[i].xx.x >= 0 && btm[i].yy.x >= 0), function main, file video.c, line 63.
I think your 'not negative' checks should be revised to:
            if (top[i].xx.x < 0)
                top[i].xx.x += 240;
            if (top[i].yy.x < 0)
                top[i].yy.x += 240;
            if (btm[i].xx.x < 0)
                btm[i].xx.x += 240;
            if (btm[i].yy.x < 0)
                btm[i].yy.x += 240;
This stops anything going negative.  However, it is perfectly plausible that you should simply be checking on the bottom-right x-coordinate (instead of the top-left coordinate) using the original block.  Or the wraparound may need to be more complex altogether.  That's for you to decipher.  But I think that the odd displays occur because you were providing negative values where you didn't intend to and weren't supposed to.
The key points to note here are:
- When you're debugging an algorithm, you don't have to use the normal display mechanisms.
 
- When you're debugging, reduce loop sizes where you can (
size == 2). 
- Printing just the relevant information (here, the x-coordinates) helped reduce the output.
 
- Putting the counter code to limit the amount of output simplifies things.
 
- If things are going wrong, look for patterns in what is going wrong early.
 
I had various versions of the drawRect() function before I got to the design shown, which works well on a wide screen (eg 120x65) terminal window.