my 2cents help... as I did not really not understand the whole stuff

according to your draw and if I understand right... may be this one is wrong :
1 2 3
| } else if(map.onSlope(x + sizeW / 2, y + 1) && !jumping) { onSlope = true;
|
no ?
"y+1" may be replaced by "y-1 or - 2 - 3" ? or something like that
"y + 1" is intended to check for slope below player, wouldn't y-1, -2 be checking the slope above player? I think my problem happens when entering/exiting the slope, so I'm doing the check suggested by Nate now and I'll post back with the results. Thanks again for the help =)
Here are the test results:
Note:
- checkX/checkY is the X/Y position to check slope collision(where the white square is)
- onSlope is a boolean to tell if player is currently on a slope
- playerX/playerY is the current position of player(top left of the blue square)
1) Entering slope from a higher tile, from tile 6 -> 7 in X direction, tile 2 -> 3 in Y direction

checkX checkY onSlope playerX playerY
6.0249996 2.96 false 5.7 2.31
6.0249996 2.96 false 5.7 2.31
6.0249996 2.96 false 5.7 2.31
6.0249996 2.96 false 5.7 2.31
6.0249996 2.96 false 5.7 2.31
2) When player X is somewhere near 6.0, the jump bug occurs (5.99999999..../6.0111111111..... will cause this problem too)
checkX checkY onSlope playerX playerY
6.325 2.96 false 6.0 2.31
6.325 2.96 false 6.0 2.31
6.325 2.96 false 6.0 2.31
6.325 2.96 false 6.0 2.31
6.325 2.96 false 6.0 2.31
6.325 2.96 false 6.0 2.31
6.325 2.96 false 6.0 2.31
6.325 3.8730001 true 6.0 2.3249998
6.325 2.975 false 6.0 2.3249998
6.325 2.975 false 6.0 2.3249998
6.325 2.975 false 6.0 2.3249998
6.325 2.975 false 6.0 2.3249998
6.325 2.975 false 6.0 2.3249998
6.325 3.8525 true 6.0 2.3249998
3)From playerX = 6.1 onwards everything is fine, the first couple onSlope = false is when player is falling onto the slope.

checkX checkY onSlope playerX playerY
6.4249997 2.96 false 6.1 2.31
6.4249997 2.96 false 6.1 2.31
6.4249997 2.96 false 6.1 2.31
6.4249997 2.96 false 6.1 2.31
6.4249997 2.96 false 6.1 2.31
6.4249997 2.96 false 6.1 2.31
6.4249997 2.96 false 6.1 2.31
6.4249997 3.8725 true 6.1 2.4249997
6.4249997 3.0749998 true 6.1 2.4249997
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6.4249997 3.0749998 true 6.1 2.4249997