As others have said, there are different types of cast on and this will leave the tail at one end or the other on your needle. It probably doesn’t matter which cast on you used or which end of the work the tail is hanging so long as you have done the rows as stated in the pattern and then use the vvvvvvv side as the right side.
Often the cast on edge gets seamed in to another edge and is therefore hidden anyway, in patterns where it is not hidden the pattern might state to use a particular type of cast on for decorative purposes or because the edge is returned to later on (such as a provisional cast on which holds stitches so they can be picked up and worked in the opposite direction, or bound off with another edge to join two pieces together). Even in patterns which state which cast on to use, depending on the reasoning for it being stated, oftentimes it can be changed based on personal preference and will not impact the project negatively.
Different cast on methods result in the stitches being on one of the needles but this could be the left needle or the right needle. Being on the left needle means the stitches are in position to begin working without turning the work. Being on the right needle means the work is turned before beginning to work the stitches- that’s why the tail may be at one end or the other.
There is a knit side and a purl side to cast on edges but it is not going to make a massive difference to your finished project if the cast on shows the purl side rather than the knit side. It is something that an experienced knitter might care about, or a perfectionist, but it makes very little difference unless the cast on was an elaborate decorative lace cast on or picot or scalloped cast on in which case it would matter a great deal to get it showing the right side.
Another thing to note is not all "row 1"s are right side of the work. Row 1 might mean right side or wrong side and this will change per pattern.
All in all, for what you are making there is no need to worry about the cast on edge or where the tail is. Only that you have worked the rows as given and the correct number of them.
Sometimes a tail is used to seam something up. If your pattern says use the tail to seam and your tail is in the wrong position this does not matter. A new piecenofnyarn can be used to seam the work and all yarn ends can be weaved in to secure them in the the wrong side of the fabric.
Hope this helps.
I remember my own question over the confusion of which was the right side and wrong side of a cast on edge and I have since learned how to identify the edge and also have the confidence to change a cast on or bind off edge to one I think will work better.