How can I prevent my pom poms made by fork method to not look separated in the middle?
I googled 'fork made pompom' and now understand better what you are asking about. This is the random site I used, (as I prefer still pictures over videos.) I have no connection to this site.
There are four options for mistakes I see:

Not enough windings for the size of your yarn compared to your fork.
Not pulled together enough when tying the middle.
Too many wraps of the tying yarn compared to the size of the pompom.
Not cut right when the sides are cut open.

The instructions I found mentioned '50' times wound around the tines of the fork. No adjustments to the size of the yarn or the fork. If you use a bigger fork and thinner yarn, you may end up with a 'thin' pompom, which will not fill out to a full ball. You can experiment with more winding before you cut and tie off the pompom.
So the improvement solution is to add more windings to the fork before tying off.
When you tie the yarn together in the middle, you have to pull very hard, getting all the air out of all the strands of yarn and from between them. It is not easy to get that right the first time you try, and when you do not tie tight enough the resulting pompom will not form right. It will also be easy to pull yarns out of the ball, likely resulting with completely destroying the pompom in a few yarns picked out. When tied tight enough you can improve almost every pompom into a good ball, by cutting it short enough.
The improvement solution here is to tie tighter than you have done before. Going to the level where you are afraid of breaking your yarn. Or even by replacing your pompom yarn with a stronger kind of yarn which you can pull on more.
Even while you have to tie tight and strong, you should not have a wide strip of yarn around your pompom before you cut it.
Switching to a stronger yarn may help you to use less wide strips of yarn.
Cutting your pompom into a nice ball is important but if it starts with a good filled tightly tied center, you can easily see how to improve the final shape.
When just cut open at the sides you will likely have tufts sticking out which might look like 'divided in the middle' but this is the least likely reason.
But if you made a mistake here, cutting into a smaller ball should result in a better pompom.
You can improve the results of pompoms by brushing out the yarns but when properly made, you should not need to.
If you can not get your fork pompoms to work, there are several other methods, like simple card rings which you can make yourself and plastic rings where you have two halves which you combine into a ring later and likely some more. With all of those you have more options for sizes and often more control on the quality of the pompom. (And you will likely have less to cut off when you make it into a nice ball.)