I hate those dotted line rows too!

I hope you are not knitting with more than one colour at a time, because that will require a different answer than the one I am going to write.

It does not matter at all which colour is on top when you change colours.

With garter stitch (knitting all of the stitches) or when all of the rows are purled, the thing that matters - to keep all the dotted line rows on one side of the knitted piece - is that you always start your different colour on the same side as the previous colour change(s).
To be perfectly technical about it - you can only change colours after you have knit an even number of rows (after 2 rows, or 4 rows, or 6 rows, etc.)
Or only after an odd number of rows - after 3 rows, 5 rows, 7, etc.

You did not say if the pattern is all garter stitch (all knit stitches) or if it is stockinette stitch (knit a row, then purl a row). With stockinette stitch, I can't remember right off the top of my head ... but the same sort of principle applies. Colour change(s) must only be done after the purl row (I think) so the dotted rows only appear on the wrong side of the knitted piece. (If that is wrong, then the colour change can only be done after the knitted row.) Try it and see.