If you are fertilizing the seedlings, you will be fine, but the ingredients in the mix you bought are basically just pH balanced Canadian sphagnum peat moss and wood pulp (which have about zero usable nutrients), so you are definitely going to run into trouble without fertilizer. It is always good to find out whether or not your growing media is fortified with fertilizer before using it.
Usually the biggest difference between potting mix and seed starting mix is porosity. The seed starting mix will generally be lighter and freer draining in comparison with bagged potting mix. This is not ways the case, though, and you can repot into seed starter if you want, you'll just have to possibly water and fertilize more often.
Apple seedlings tend to grow best in well fertilized soils, so use something with plenty of at least the 'main' three nutrients, or npk. Of course, if you can find a micronutrient complex and some minerals as well, that would be best (the mix doesn't contain many of those either).