From Magento there is a feature called Blocks Permission that allows the defined block can be display in CMS page / CMS static blocks.

If you don't see the Product slider display correctly in CMS page, then look at the System > Permissions > Blocks

If there is no block called productslider/productslider or similar that name, so you have to add it into this grid.

Click on Add new block  > Fill as the following:

then click save.

Now go to frontend and see the changes.

If you have any problem, feel free to create a topic