This is probably just because the coins aren’t actually fair. If the coin is slightly biased towards heads, the first throw is more likely to heads, and so are all subsequent throws. Same for tails.
That's not the problem. You can test that by using a highly secure random number generator, e.g. /dev/random in Linux, to select the initial side. Keep track of that initial side, record the side it lands on. This paper shows a same-side bias, not a heads bias.
A same side bias is either a heads bias or a tails bias.