Yes the petroleum jelly and Vaseline does help to darken skin especially if you use the petroleum jelly daily.
The petroleum jelly is also a good natural skin moisturizer and helps with dry skin and also helps to hold moisture in your skin as well to prevent your skin from drying out.
If you continue to use petroleum jelly daily or at least every few days then within a month or two months you should have darker skin as a result.
Just avoid overusing petroleum jelly on your skin though because it can clog your skins pores but if you use just enough to moisturize your skin then it should be okay.
I got darker skin within 2 months after using the petroleum jelly on my skin and I use it on my arms and legs to help keep moisture in the skin to prevent them from drying out.
I also like to add some petroleum jelly to my feet to help keep the feet from drying out and cracking and it prevents rashes and sores on my feet as well.