You all getting in the weeds with poor excuses for this game mechanic. I will leave you with a solution and I will start dismounting when I get next to a bad guy so Im not nerfed compared to other animal companion users.
If your companion moved on it current turn it shares map. If it did not move on its current turn it does not share map
Also a mount still can count as cover even if you are not riding it and it can be a flank buddy if you are not mounted on it. So these things go both ways...give and take
Read all my replys before you comment anymore please and thank you