This can happen 30 minutes later or even many hours later after a shower is taken. The new shower fixture installed didn't solve the problem. Can anything be done to correct this and prevent this surge of water?
By surge of water, I'm guessing you mean a quick trickle that would fill a cup and not a hard spray that would let you wash your hair. Like Steven says, the shower head will still have water in it after you shut off the water.
My guess for why you see the surge is that the water is held in the shower head by water tension at each of the nozzles. Eventually that breaks from vibration, water contracting as it cools, or drying out. This allows air to be sucked into the shower head while water drains out the rest of the nozzles.
There's nothing much to fix. But if it bothers you, give it a shake or run your finger over the nozzles to break the surface tension. Another suggestion is to make sure your shower head is mounted at an angle, rather than spraying downwards.
There is usually still some water left in the shower head due to how they are designed. Mine has a number of pivots in it, and if I point it directly down, a fair amount of water will pour out after it has been off for some time.
My guess is that changes in atmospheric pressure cause the water to come out of the shower head after-the-fact. If you watch your toilets sometimes you can see the water level rise and fall slightly too.
I'm not sure why it's an issue that needs to be "resolved", but if you get a detachable shower head, then you can just hang the shower head from the flexible pipe and all of the water will come out.
Some bath fixtures have a diverter (the gadget that directs water to either the faucet or the shower head) that is designed so that if you put it into the "shower" position, it will stay there until you either manually set it to "faucet" or you turn off the water. They typically look like a knob on the top of the faucet.
Once you turn off the water, gravity pulls the diverter back into the "faucet" position, and any water remaining in the pipe up to and in the shower head simply falls back down and out the faucet.
Over time, the diverter can get gummed up with soap scum or hard water deposits, making it hard to move freely on its own. If this happens, the water stays in the pipes until one of the events @BMitch describes occurs.
You should be able to get it to move more freely by opening and closing the diverter several times. If that's not enough, I've also had some luck with spraying Scrubbing Bubbles foaming cleaner where the stem of the diverter enters the faucet, letting it sit for a few minutes, then opening and closing the diverter.