I have no idea if it's the intended design.
But note also that if units join your army in the field (and not in a city) that they will not see any benefit from tireless march unless you recast it. So even if it's not by design I think it's a feature because it's better than having to pay additional mana to bring a new unit up to speed.
I'm pretty sure that's wrong. I run a stack full of champions, who all have tireless march cast on them. It's worth the 9 mana upkeep to me to have 13 movement points. Anyway, if you leave a city or have a unit join the main stack in the field, the movement gets set to the lowest value of any unit present. So say you have 3 champs with horses, and one of them has tireless march. If you move into and out of a city that turn, the movement will be set to 4 because that's the speed of the slowest unit. The next turn they will have a movement of 5 because the two without tireless march get the benefit from it. If they all three have horses and tireless march, the movement upon exiting the city will be 5. The next turn it will be 7 because of the stacking of tireless march. However, unless you click to each of the units individually within that army, the movement the next turn may only be 5/7 instead of 7/7. Whenever I exit a city it will show a movement of 5, but then when I click to each unit their individual points will show up the true value, and when you're done click back to the army leader and it should show you the right value. The army's speed will always show the value of the slowest member. So say you have that same 3 champ army and you add a 4th member to it out in the field. It's a hero with a horse but without tireless march. You had him sitting right next to the main army, so he only uses 1 Movement point to get in, so the army will show that you have only 3/4 movement left that turn. If you click to each member of the army, you will see their movement goes up to 3/7, and when you have cycled through they will all say 3/7 and the army will be 3/7. The next turn you will get the full 7 movement points, but if you forgot to cycle through the units, you will only get 4/7. Does that make sense? I don't mean does it make sense to have it that way, rather, do you understand the concept? (it doesn't really make sense to me to have it the way they do, but I don't know how to suggest they fix it so I just live with it)